LMFDB - Embedded newform 14.14.c.b.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,14,Mod(9,14)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 14, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("14.9");

S:= CuspForms(chi, 14);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	14.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.0123300533$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 209077 x^{6} - 47718852 x^{5} + 40973427094 x^{4} - 4988457209802 x^{3} + \cdots + 75\!\cdots\!25 $ x^8 + 209077x^6 - 47718852x^5 + 40973427094x^4 - 4988457209802x^3 + 1142094021456771x^2 + 65369216338084710x + 7506311351102577225
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{14}\cdot 3\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.1
Root			$-35.6648 + 61.7733i$ of defining polynomial
Character	$\chi$	$=$	14.11
Dual form			14.14.c.b.9.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(32.0000 + 55.4256i) q^{2} +(-746.854 + 1293.59i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-7178.20 - 12433.0i) q^{5} -95597.3 q^{6} +(-302505. + 73348.4i) q^{7} -262144. q^{8} +(-318420. - 551520. i) q^{9} +O(q^{10})$	\(q+(32.0000 + 55.4256i) q^{2} +(-746.854 + 1293.59i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-7178.20 - 12433.0i) q^{5} -95597.3 q^{6} +(-302505. + 73348.4i) q^{7} -262144. q^{8} +(-318420. - 551520. i) q^{9} +(459405. - 795712. i) q^{10} +(2.14272e6 - 3.71130e6i) q^{11} +(-3.05911e6 - 5.29854e6i) q^{12} +5.50861e6 q^{13} +(-1.37455e7 - 1.44194e7i) q^{14} +2.14443e7 q^{15} +(-8.38861e6 - 1.45295e7i) q^{16} +(1.98554e7 - 3.43905e7i) q^{17} +(2.03789e7 - 3.52973e7i) q^{18} +(-2.25114e7 - 3.89910e7i) q^{19} +5.88038e7 q^{20} +(1.31044e8 - 4.46097e8i) q^{21} +2.74268e8 q^{22} +(-3.77343e8 - 6.53577e8i) q^{23} +(1.95783e8 - 3.39107e8i) q^{24} +(5.07299e8 - 8.78667e8i) q^{25} +(1.76275e8 + 3.05318e8i) q^{26} -1.43020e9 q^{27} +(3.59345e8 - 1.22327e9i) q^{28} -2.46353e9 q^{29} +(6.86216e8 + 1.18856e9i) q^{30} +(-3.06703e9 + 5.31225e9i) q^{31} +(5.36871e8 - 9.29888e8i) q^{32} +(3.20060e9 + 5.54359e9i) q^{33} +2.54149e9 q^{34} +(3.08338e9 + 3.23453e9i) q^{35} +2.60850e9 q^{36} +(9.52417e9 + 1.64963e10i) q^{37} +(1.44073e9 - 2.49542e9i) q^{38} +(-4.11413e9 + 7.12588e9i) q^{39} +(1.88172e9 + 3.25924e9i) q^{40} -4.23093e10 q^{41} +(2.89186e10 - 7.01191e9i) q^{42} -7.42867e10 q^{43} +(8.77657e9 + 1.52015e10i) q^{44} +(-4.57137e9 + 7.91784e9i) q^{45} +(2.41499e10 - 4.18289e10i) q^{46} +(-4.03508e10 - 6.98897e10i) q^{47} +2.50603e10 q^{48} +(8.61290e10 - 4.43764e10i) q^{49} +6.49342e10 q^{50} +(2.96581e10 + 5.13694e10i) q^{51} +(-1.12816e10 + 1.95404e10i) q^{52} +(1.10539e11 - 1.91459e11i) q^{53} +(-4.57664e10 - 7.92697e10i) q^{54} -6.15234e10 q^{55} +(7.92998e10 - 1.92278e10i) q^{56} +6.72511e10 q^{57} +(-7.88329e10 - 1.36543e11i) q^{58} +(-2.29890e11 + 3.98181e11i) q^{59} +(-4.39178e10 + 7.60679e10i) q^{60} +(-3.23925e10 - 5.61055e10i) q^{61} -3.92580e11 q^{62} +(1.36777e11 + 1.43482e11i) q^{63} +6.87195e10 q^{64} +(-3.95419e10 - 6.84885e10i) q^{65} +(-2.04838e11 + 3.54790e11i) q^{66} +(2.07214e11 - 3.58905e11i) q^{67} +(8.13276e10 + 1.40864e11i) q^{68} +1.12728e12 q^{69} +(-8.06078e10 + 2.74403e11i) q^{70} -6.38110e11 q^{71} +(8.34720e10 + 1.44578e11i) q^{72} +(-2.92998e11 + 5.07488e11i) q^{73} +(-6.09547e11 + 1.05577e12i) q^{74} +(7.57756e11 + 1.31247e12i) q^{75} +1.84414e11 q^{76} +(-3.75965e11 + 1.27985e12i) q^{77} -5.26608e11 q^{78} +(-1.22943e12 - 2.12943e12i) q^{79} +(-1.20430e11 + 2.08591e11i) q^{80} +(1.57581e12 - 2.72939e12i) q^{81} +(-1.35390e12 - 2.34502e12i) q^{82} +3.32114e12 q^{83} +(1.31404e12 + 1.37845e12i) q^{84} -5.70103e11 q^{85} +(-2.37717e12 - 4.11739e12i) q^{86} +(1.83990e12 - 3.18679e12i) q^{87} +(-5.61701e11 + 9.72894e11i) q^{88} +(1.39203e12 + 2.41106e12i) q^{89} -5.85135e11 q^{90} +(-1.66638e12 + 4.04047e11i) q^{91} +3.09119e12 q^{92} +(-4.58125e12 - 7.93495e12i) q^{93} +(2.58245e12 - 4.47294e12i) q^{94} +(-3.23183e11 + 5.59770e11i) q^{95} +(8.01928e11 + 1.38898e12i) q^{96} -7.80467e12 q^{97} +(5.21572e12 + 3.35371e12i) q^{98} -2.72914e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 256 q^{2} + 182 q^{3} - 16384 q^{4} + 1792 q^{5} + 23296 q^{6} - 268352 q^{7} - 2097152 q^{8} + 599840 q^{9}+O(q^{10}) $ 8 * q + 256 * q^2 + 182 * q^3 - 16384 * q^4 + 1792 * q^5 + 23296 * q^6 - 268352 * q^7 - 2097152 * q^8 + 599840 * q^9	\( 8 q + 256 q^{2} + 182 q^{3} - 16384 q^{4} + 1792 q^{5} + 23296 q^{6} - 268352 q^{7} - 2097152 q^{8} + 599840 q^{9} - 114688 q^{10} - 8726914 q^{11} + 745472 q^{12} + 1438416 q^{13} + 27004544 q^{14} - 136873212 q^{15} - 67108864 q^{16} - 7943068 q^{17} - 38389760 q^{18} - 215706806 q^{19} - 14680064 q^{20} - 414124312 q^{21} - 1117044992 q^{22} - 61927978 q^{23} - 47710208 q^{24} - 1327844792 q^{25} + 46029312 q^{26} - 3268643812 q^{27} + 2827460608 q^{28} - 6325846064 q^{29} - 4379942784 q^{30} + 6113775570 q^{31} + 4294967296 q^{32} + 25235960652 q^{33} - 1016712704 q^{34} + 41542225382 q^{35} - 4913889280 q^{36} - 3945652880 q^{37} + 13805235584 q^{38} - 23545599116 q^{39} - 469762048 q^{40} + 86378579952 q^{41} + 16061065216 q^{42} - 109074124256 q^{43} - 35745439744 q^{44} - 104964468168 q^{45} + 3963390592 q^{46} - 3141202722 q^{47} - 6106906624 q^{48} + 151080461672 q^{49} - 169964133376 q^{50} - 241278267462 q^{51} - 2945875968 q^{52} + 149625680376 q^{53} - 104596601984 q^{54} + 174912009748 q^{55} + 70346866688 q^{56} - 128207489960 q^{57} - 202427074048 q^{58} - 866297313938 q^{59} + 280316338176 q^{60} - 477908594184 q^{61} + 782563272960 q^{62} + 953051390564 q^{63} + 549755813888 q^{64} - 1099748343120 q^{65} - 1615101481728 q^{66} + 1895501016278 q^{67} - 32534806528 q^{68} + 3503301895632 q^{69} + 1443396653440 q^{70} + 638832672128 q^{71} - 157244456960 q^{72} - 2966596192756 q^{73} + 252521784320 q^{74} - 1331079867376 q^{75} + 1767070154752 q^{76} + 6943031627392 q^{77} - 3013836686848 q^{78} - 6505959677634 q^{79} + 30064771072 q^{80} + 2449216493684 q^{81} + 2764114558464 q^{82} - 3379817135968 q^{83} + 2724161355776 q^{84} - 16684556982464 q^{85} - 3490371976192 q^{86} - 5273311164492 q^{87} + 2287708143616 q^{88} + 9586601667468 q^{89} - 13435451925504 q^{90} + 16069253407200 q^{91} + 507313995776 q^{92} - 14195747226896 q^{93} + 201036974208 q^{94} + 14384410136978 q^{95} - 195421011968 q^{96} - 44560735311568 q^{97} - 2146516623104 q^{98} + 24706419985464 q^{99}+O(q^{100}) \) 8 * q + 256 * q^2 + 182 * q^3 - 16384 * q^4 + 1792 * q^5 + 23296 * q^6 - 268352 * q^7 - 2097152 * q^8 + 599840 * q^9 - 114688 * q^10 - 8726914 * q^11 + 745472 * q^12 + 1438416 * q^13 + 27004544 * q^14 - 136873212 * q^15 - 67108864 * q^16 - 7943068 * q^17 - 38389760 * q^18 - 215706806 * q^19 - 14680064 * q^20 - 414124312 * q^21 - 1117044992 * q^22 - 61927978 * q^23 - 47710208 * q^24 - 1327844792 * q^25 + 46029312 * q^26 - 3268643812 * q^27 + 2827460608 * q^28 - 6325846064 * q^29 - 4379942784 * q^30 + 6113775570 * q^31 + 4294967296 * q^32 + 25235960652 * q^33 - 1016712704 * q^34 + 41542225382 * q^35 - 4913889280 * q^36 - 3945652880 * q^37 + 13805235584 * q^38 - 23545599116 * q^39 - 469762048 * q^40 + 86378579952 * q^41 + 16061065216 * q^42 - 109074124256 * q^43 - 35745439744 * q^44 - 104964468168 * q^45 + 3963390592 * q^46 - 3141202722 * q^47 - 6106906624 * q^48 + 151080461672 * q^49 - 169964133376 * q^50 - 241278267462 * q^51 - 2945875968 * q^52 + 149625680376 * q^53 - 104596601984 * q^54 + 174912009748 * q^55 + 70346866688 * q^56 - 128207489960 * q^57 - 202427074048 * q^58 - 866297313938 * q^59 + 280316338176 * q^60 - 477908594184 * q^61 + 782563272960 * q^62 + 953051390564 * q^63 + 549755813888 * q^64 - 1099748343120 * q^65 - 1615101481728 * q^66 + 1895501016278 * q^67 - 32534806528 * q^68 + 3503301895632 * q^69 + 1443396653440 * q^70 + 638832672128 * q^71 - 157244456960 * q^72 - 2966596192756 * q^73 + 252521784320 * q^74 - 1331079867376 * q^75 + 1767070154752 * q^76 + 6943031627392 * q^77 - 3013836686848 * q^78 - 6505959677634 * q^79 + 30064771072 * q^80 + 2449216493684 * q^81 + 2764114558464 * q^82 - 3379817135968 * q^83 + 2724161355776 * q^84 - 16684556982464 * q^85 - 3490371976192 * q^86 - 5273311164492 * q^87 + 2287708143616 * q^88 + 9586601667468 * q^89 - 13435451925504 * q^90 + 16069253407200 * q^91 + 507313995776 * q^92 - 14195747226896 * q^93 + 201036974208 * q^94 + 14384410136978 * q^95 - 195421011968 * q^96 - 44560735311568 * q^97 - 2146516623104 * q^98 + 24706419985464 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	32.0000	+	55.4256i	0.353553	+	0.612372i
$2$	32.0000	+	55.4256i	0.353553	+	0.612372i
$3$	−746.854	+	1293.59i	−0.591490	+	1.02449i	0.402542	+	0.915402i	$0.368127\pi$
$3$	−746.854	+	1293.59i	−0.591490	+	1.02449i	−0.994032	+	0.109090i	$0.965206\pi$
$4$	−2048.00	+	3547.24i	−0.250000	+	0.433013i
$5$	−7178.20	−	12433.0i	−0.205452	−	0.355853i	0.744825	−	0.667260i	$-0.232533\pi$
$5$	−7178.20	−	12433.0i	−0.205452	−	0.355853i	−0.950277	+	0.311407i	$0.899200\pi$
$6$	−95597.3			−0.836494
$7$	−302505.	+	73348.4i	−0.971840	+	0.235642i
$7$	−302505.	+	73348.4i	−0.971840	+	0.235642i
$8$	−262144.			−0.353553
$9$	−318420.	−	551520.i	−0.199721	−	0.345928i
$10$	459405.	−	795712.i	0.145276	−	0.251626i
$11$	2.14272e6	−	3.71130e6i	0.364681	−	0.631645i	−0.624044	−	0.781389i	$-0.714512\pi$
$11$	2.14272e6	−	3.71130e6i	0.364681	−	0.631645i	0.988725	+	0.149744i	$0.0478449\pi$
$12$	−3.05911e6	−	5.29854e6i	−0.295745	−	0.512246i
$13$	5.50861e6			0.316527			0.158263	−	0.987397i	$-0.449411\pi$
$13$	5.50861e6			0.316527			0.158263	+	0.987397i	$0.449411\pi$
$14$	−1.37455e7	−	1.44194e7i	−0.487898	−	0.511816i
$15$	2.14443e7			0.486091
$16$	−8.38861e6	−	1.45295e7i	−0.125000	−	0.216506i
$17$	1.98554e7	−	3.43905e7i	0.199508	−	0.345558i	−0.748861	−	0.662727i	$-0.769399\pi$
$17$	1.98554e7	−	3.43905e7i	0.199508	−	0.345558i	0.948369	+	0.317169i	$0.102732\pi$
$18$	2.03789e7	−	3.52973e7i	0.141224	−	0.244608i
$19$	−2.25114e7	−	3.89910e7i	−0.109775	−	0.190137i	0.805904	−	0.592046i	$-0.201680\pi$
$19$	−2.25114e7	−	3.89910e7i	−0.109775	−	0.190137i	−0.915679	+	0.401910i	$0.868346\pi$
$20$	5.88038e7			0.205452
$21$	1.31044e8	−	4.46097e8i	0.333420	−	1.13502i
$22$	2.74268e8			0.515736
$23$	−3.77343e8	−	6.53577e8i	−0.531502	−	0.920589i	−0.999324	−	0.0367661i	$-0.988294\pi$
$23$	−3.77343e8	−	6.53577e8i	−0.531502	−	0.920589i	0.467822	−	0.883823i	$-0.345039\pi$
$24$	1.95783e8	−	3.39107e8i	0.209123	−	0.362212i
$25$	5.07299e8	−	8.78667e8i	0.415579	−	0.719804i
$26$	1.76275e8	+	3.05318e8i	0.111909	+	0.193832i
$27$	−1.43020e9			−0.710447
$28$	3.59345e8	−	1.22327e9i	0.140924	−	0.479730i
$29$	−2.46353e9			−0.769078			−0.384539	−	0.923109i	$-0.625640\pi$
$29$	−2.46353e9			−0.769078			−0.384539	+	0.923109i	$0.625640\pi$
$30$	6.86216e8	+	1.18856e9i	0.171859	+	0.297669i
$31$	−3.06703e9	+	5.31225e9i	−0.620679	+	1.07505i	0.368681	+	0.929556i	$0.379810\pi$
$31$	−3.06703e9	+	5.31225e9i	−0.620679	+	1.07505i	−0.989360	+	0.145491i	$0.953524\pi$
$32$	5.36871e8	−	9.29888e8i	0.0883883	−	0.153093i
$33$	3.20060e9	+	5.54359e9i	0.431410	+	0.747224i
$34$	2.54149e9			0.282147
$35$	3.08338e9	+	3.23453e9i	0.283520	+	0.297419i
$36$	2.60850e9			0.199721
$37$	9.52417e9	+	1.64963e10i	0.610261	+	1.05700i	0.991196	+	0.132401i	$0.0422688\pi$
$37$	9.52417e9	+	1.64963e10i	0.610261	+	1.05700i	−0.380935	+	0.924602i	$0.624398\pi$
$38$	1.44073e9	−	2.49542e9i	0.0776229	−	0.134447i
$39$	−4.11413e9	+	7.12588e9i	−0.187222	+	0.324279i
$40$	1.88172e9	+	3.25924e9i	0.0726382	+	0.125813i
$41$	−4.23093e10			−1.39104			−0.695522	−	0.718505i	$-0.744827\pi$
$41$	−4.23093e10			−1.39104			−0.695522	+	0.718505i	$0.744827\pi$
$42$	2.89186e10	−	7.01191e9i	0.812938	−	0.197113i
$43$	−7.42867e10			−1.79212			−0.896058	−	0.443937i	$-0.853581\pi$
$43$	−7.42867e10			−1.79212			−0.896058	+	0.443937i	$0.853581\pi$
$44$	8.77657e9	+	1.52015e10i	0.182340	+	0.315823i
$45$	−4.57137e9	+	7.91784e9i	−0.0820663	+	0.142143i
$46$	2.41499e10	−	4.18289e10i	0.375829	−	0.650955i
$47$	−4.03508e10	−	6.98897e10i	−0.546030	−	0.945751i	−0.998541	−	0.0539926i	$-0.982805\pi$
$47$	−4.03508e10	−	6.98897e10i	−0.546030	−	0.945751i	0.452512	−	0.891758i	$-0.350528\pi$
$48$	2.50603e10			0.295745
$49$	8.61290e10	−	4.43764e10i	0.888945	−	0.458013i
$50$	6.49342e10			0.587717
$51$	2.96581e10	+	5.13694e10i	0.236014	+	0.408788i
$52$	−1.12816e10	+	1.95404e10i	−0.0791316	+	0.137060i
$53$	1.10539e11	−	1.91459e11i	0.685049	−	1.18654i	−0.288372	−	0.957518i	$-0.593114\pi$
$53$	1.10539e11	−	1.91459e11i	0.685049	−	1.18654i	0.973421	−	0.229021i	$-0.0735526\pi$
$54$	−4.57664e10	−	7.92697e10i	−0.251181	−	0.435058i
$55$	−6.15234e10			−0.299697
$56$	7.92998e10	−	1.92278e10i	0.343597	−	0.0833121i
$57$	6.72511e10			0.259724
$58$	−7.88329e10	−	1.36543e11i	−0.271910	−	0.470962i
$59$	−2.29890e11	+	3.98181e11i	−0.709548	+	1.22897i	0.255477	+	0.966815i	$0.417767\pi$
$59$	−2.29890e11	+	3.98181e11i	−0.709548	+	1.22897i	−0.965025	+	0.262158i	$0.915566\pi$
$60$	−4.39178e10	+	7.60679e10i	−0.121523	+	0.210484i
$61$	−3.23925e10	−	5.61055e10i	−0.0805009	−	0.139432i	0.822964	−	0.568093i	$-0.192319\pi$
$61$	−3.23925e10	−	5.61055e10i	−0.0805009	−	0.139432i	−0.903465	+	0.428661i	$0.858985\pi$
$62$	−3.92580e11			−0.877772
$63$	1.36777e11	+	1.43482e11i	0.275612	+	0.289123i
$64$	6.87195e10			0.125000
$65$	−3.95419e10	−	6.84885e10i	−0.0650310	−	0.112637i
$66$	−2.04838e11	+	3.54790e11i	−0.305053	+	0.528367i
$67$	2.07214e11	−	3.58905e11i	0.279855	−	0.484722i	−0.691494	−	0.722382i	$-0.743047\pi$
$67$	2.07214e11	−	3.58905e11i	0.279855	−	0.484722i	0.971348	+	0.237660i	$0.0763804\pi$
$68$	8.13276e10	+	1.40864e11i	0.0997540	+	0.172779i
$69$	1.12728e12			1.25751
$70$	−8.06078e10	+	2.74403e11i	−0.0818917	+	0.278774i
$71$	−6.38110e11			−0.591175			−0.295588	−	0.955316i	$-0.595515\pi$
$71$	−6.38110e11			−0.591175			−0.295588	+	0.955316i	$0.595515\pi$
$72$	8.34720e10	+	1.44578e11i	0.0706122	+	0.122304i
$73$	−2.92998e11	+	5.07488e11i	−0.226603	+	0.392488i	−0.956799	−	0.290749i	$-0.906095\pi$
$73$	−2.92998e11	+	5.07488e11i	−0.226603	+	0.392488i	0.730196	+	0.683238i	$0.239429\pi$
$74$	−6.09547e11	+	1.05577e12i	−0.431520	+	0.747414i
$75$	7.57756e11	+	1.31247e12i	0.491622	+	0.851514i
$76$	1.84414e11			0.109775
$77$	−3.75965e11	+	1.27985e12i	−0.205569	+	0.699792i
$78$	−5.26608e11			−0.264772
$79$	−1.22943e12	−	2.12943e12i	−0.569019	−	0.985571i	−0.996663	−	0.0816233i	$-0.973990\pi$
$79$	−1.22943e12	−	2.12943e12i	−0.569019	−	0.985571i	0.427644	−	0.903947i	$-0.359344\pi$
$80$	−1.20430e11	+	2.08591e11i	−0.0513630	+	0.0889633i
$81$	1.57581e12	−	2.72939e12i	0.619944	−	1.07377i
$82$	−1.35390e12	−	2.34502e12i	−0.491808	−	0.851837i
$83$	3.32114e12			1.11501			0.557506	−	0.830173i	$-0.311758\pi$
$83$	3.32114e12			1.11501			0.557506	+	0.830173i	$0.311758\pi$
$84$	1.31404e12	+	1.37845e12i	0.408124	+	0.428131i
$85$	−5.70103e11			−0.163957
$86$	−2.37717e12	−	4.11739e12i	−0.633609	−	1.09744i
$87$	1.83990e12	−	3.18679e12i	0.454902	−	0.787913i
$88$	−5.61701e11	+	9.72894e11i	−0.128934	+	0.223320i
$89$	1.39203e12	+	2.41106e12i	0.296902	+	0.514249i	0.975426	−	0.220329i	$-0.0707132\pi$
$89$	1.39203e12	+	2.41106e12i	0.296902	+	0.514249i	−0.678523	+	0.734579i	$0.737380\pi$
$90$	−5.85135e11			−0.116059
$91$	−1.66638e12	+	4.04047e11i	−0.307613	+	0.0745870i
$92$	3.09119e12			0.531502
$93$	−4.58125e12	−	7.93495e12i	−0.734251	−	1.27176i
$94$	2.58245e12	−	4.47294e12i	0.386101	−	0.668747i
$95$	−3.23183e11	+	5.59770e11i	−0.0451071	+	0.0781279i
$96$	8.01928e11	+	1.38898e12i	0.104562	+	0.181106i
$97$	−7.80467e12			−0.951345			−0.475672	−	0.879622i	$-0.657795\pi$
$97$	−7.80467e12			−0.951345			−0.475672	+	0.879622i	$0.657795\pi$
$98$	5.21572e12	+	3.35371e12i	0.594764	+	0.382434i
$99$	−2.72914e12			−0.291338
$100$	2.07789e12	+	3.59902e12i	0.207789	+	0.359902i
$101$	−6.58305e12	+	1.14022e13i	−0.617076	+	1.06881i	0.372941	+	0.927855i	$0.378349\pi$
$101$	−6.58305e12	+	1.14022e13i	−0.617076	+	1.06881i	−0.990017	+	0.140951i	$0.954984\pi$
$102$	−1.89812e12	+	3.28764e12i	−0.166887	+	0.289057i
$103$	8.84393e12	+	1.53181e13i	0.729799	+	1.26405i	0.956968	+	0.290194i	$0.0937199\pi$
$103$	8.84393e12	+	1.53181e13i	0.729799	+	1.26405i	−0.227168	+	0.973855i	$0.572947\pi$
$104$	−1.44405e12			−0.111909
$105$	−6.48699e12	+	1.57290e12i	−0.472403	+	0.114544i
$106$	1.41490e13			0.968806
$107$	7.23079e12	+	1.25241e13i	0.465791	+	0.806774i	0.999237	−	0.0390602i	$-0.0124364\pi$
$107$	7.23079e12	+	1.25241e13i	0.465791	+	0.806774i	−0.533446	+	0.845834i	$0.679103\pi$
$108$	2.92905e12	−	5.07326e12i	0.177612	−	0.307633i
$109$	7.96586e12	−	1.37973e13i	0.454947	−	0.787991i	−0.543738	−	0.839255i	$-0.682992\pi$
$109$	7.96586e12	−	1.37973e13i	0.454947	−	0.787991i	0.998685	+	0.0512639i	$0.0163250\pi$
$110$	−1.96875e12	−	3.40997e12i	−0.105959	−	0.183526i
$111$	−2.84526e13			−1.44385
$112$	3.60331e12	+	3.77995e12i	0.172498	+	0.180954i
$113$	4.86885e12			0.219997			0.109998	−	0.993932i	$-0.464915\pi$
$113$	4.86885e12			0.219997			0.109998	+	0.993932i	$0.464915\pi$
$114$	2.15203e12	+	3.72743e12i	0.0918264	+	0.159048i
$115$	−5.41728e12	+	9.38301e12i	−0.218396	+	0.378274i
$116$	5.04530e12	−	8.73872e12i	0.192269	−	0.333020i
$117$	−1.75405e12	−	3.03811e12i	−0.0632171	−	0.109495i
$118$	−2.94259e13			−1.00345
$119$	−3.48385e12	+	1.18597e13i	−0.112462	+	0.382839i
$120$	−5.62148e12			−0.171859
$121$	8.07887e12	+	1.39930e13i	0.234016	+	0.405328i
$122$	2.07312e12	−	3.59075e12i	0.0569227	−	0.0985930i
$123$	3.15989e13	−	5.47309e13i	0.822789	−	1.42511i
$124$	−1.25626e13	−	2.17590e13i	−0.310339	−	0.537524i
$125$	−3.20908e13			−0.752430
$126$	−3.57571e12	+	1.21724e13i	−0.0796076	+	0.270998i
$127$	1.02773e12			0.0217347			0.0108674	−	0.999941i	$-0.496541\pi$
$127$	1.02773e12			0.0217347			0.0108674	+	0.999941i	$0.496541\pi$
$128$	2.19902e12	+	3.80882e12i	0.0441942	+	0.0765466i
$129$	5.54813e13	−	9.60965e13i	1.06002	−	1.83601i
$130$	2.53068e12	−	4.38327e12i	0.0459839	−	0.0796464i
$131$	3.08691e13	+	5.34668e13i	0.533654	+	0.924317i	0.999227	+	0.0393070i	$0.0125150\pi$
$131$	3.08691e13	+	5.34668e13i	0.533654	+	0.924317i	−0.465573	+	0.885010i	$0.654152\pi$
$132$	−2.62193e13			−0.431410
$133$	9.66974e12	+	1.01438e13i	0.151488	+	0.158915i
$134$	2.65234e13			0.395774
$135$	1.02662e13	+	1.77817e13i	0.145963	+	0.252815i
$136$	−5.20497e12	+	9.01527e12i	−0.0705367	+	0.122173i
$137$	6.61761e13	−	1.14620e14i	0.855102	−	1.48108i	−0.0214489	−	0.999770i	$-0.506828\pi$
$137$	6.61761e13	−	1.14620e14i	0.855102	−	1.48108i	0.876551	−	0.481310i	$-0.159839\pi$
$138$	3.60730e13	+	6.24802e13i	0.444598	+	0.770067i
$139$	−1.66284e14			−1.95548			−0.977742	−	0.209810i	$-0.932716\pi$
$139$	−1.66284e14			−1.95548			−0.977742	+	0.209810i	$0.932716\pi$
$140$	−1.77884e13	+	4.31316e12i	−0.199666	+	0.0484132i
$141$	1.20545e14			1.29188
$142$	−2.04195e13	−	3.53676e13i	−0.209012	−	0.362019i
$143$	1.18034e13	−	2.04441e13i	0.115431	−	0.199932i
$144$	−5.34221e12	+	9.25298e12i	−0.0499304	+	0.0864819i
$145$	1.76837e13	+	3.06290e13i	0.158009	+	0.273679i
$146$	−3.75038e13			−0.320465
$147$	−6.92095e12	+	1.44558e14i	−0.0565722	+	1.18163i
$148$	−7.80220e13			−0.610261
$149$	−8.54482e13	−	1.48001e14i	−0.639723	−	1.10803i	−0.985493	−	0.169714i	$-0.945716\pi$
$149$	−8.54482e13	−	1.48001e14i	−0.639723	−	1.10803i	0.345770	−	0.938319i	$-0.387618\pi$
$150$	−4.84964e13	+	8.39982e13i	−0.347629	+	0.602111i
$151$	−1.34805e14	+	2.33490e14i	−0.925458	+	1.60294i	−0.134635	+	0.990895i	$0.542986\pi$
$151$	−1.34805e14	+	2.33490e14i	−0.925458	+	1.60294i	−0.790823	+	0.612045i	$0.790347\pi$
$152$	5.90124e12	+	1.02212e13i	0.0388115	+	0.0672234i
$153$	−2.52894e13			−0.159384
$154$	−8.29673e13	+	2.01171e13i	−0.501213	+	0.121529i
$155$	8.80630e13			0.510079
$156$	−1.68515e13	−	2.91876e13i	−0.0936112	−	0.162139i
$157$	2.65409e13	−	4.59702e13i	0.141439	−	0.244979i	−0.786600	−	0.617463i	$-0.788161\pi$
$157$	2.65409e13	−	4.59702e13i	0.141439	−	0.244979i	0.928039	+	0.372484i	$0.121494\pi$
$158$	7.86834e13	−	1.36284e14i	0.402358	−	0.696904i
$159$	1.65113e14	+	2.85984e14i	0.810400	+	1.40365i
$160$	−1.54151e13			−0.0726382
$161$	1.62087e14	+	1.70033e14i	0.733465	+	0.769421i
$162$	2.01704e14			0.876733
$163$	−1.25923e14	−	2.18105e14i	−0.525878	−	0.910847i	−0.999546	−	0.0301433i	$-0.990404\pi$
$163$	−1.25923e14	−	2.18105e14i	−0.525878	−	0.910847i	0.473668	−	0.880704i	$-0.342930\pi$
$164$	8.66495e13	−	1.50081e14i	0.347761	−	0.602340i
$165$	4.59490e13	−	7.95860e13i	0.177268	−	0.307037i
$166$	1.06277e14	+	1.84076e14i	0.394216	+	0.682803i
$167$	−5.21452e12			−0.0186019			−0.00930095	−	0.999957i	$-0.502961\pi$
$167$	−5.21452e12			−0.0186019			−0.00930095	+	0.999957i	$0.502961\pi$
$168$	−3.43524e13	+	1.16942e14i	−0.117882	+	0.401291i
$169$	−2.72530e14			−0.899811
$170$	−1.82433e13	−	3.15983e13i	−0.0579676	−	0.100403i
$171$	−1.43362e13	+	2.48310e13i	−0.0438490	+	0.0759487i
$172$	1.52139e14	−	2.63513e14i	0.448029	−	0.776009i
$173$	−1.31565e14	−	2.27877e14i	−0.373113	−	0.646251i	0.616929	−	0.787019i	$-0.288376\pi$
$173$	−1.31565e14	−	2.27877e14i	−0.373113	−	0.646251i	−0.990043	+	0.140767i	$0.955043\pi$
$174$	2.35507e14			0.643329
$175$	−8.90114e13	+	3.03010e14i	−0.234260	+	0.797462i
$176$	−7.18977e13			−0.182340
$177$	−3.43388e14	−	5.94766e14i	−0.839381	−	1.45385i
$178$	−8.90899e13	+	1.54308e14i	−0.209941	+	0.363629i
$179$	1.81035e14	−	3.13562e14i	0.411357	−	0.712490i	−0.583682	−	0.811982i	$-0.698388\pi$
$179$	1.81035e14	−	3.13562e14i	0.411357	−	0.712490i	0.995038	+	0.0994921i	$0.0317218\pi$
$180$	−1.87243e13	−	3.24315e13i	−0.0410332	−	0.0710715i
$181$	−6.76438e14			−1.42994			−0.714969	−	0.699156i	$-0.753559\pi$
$181$	−6.76438e14			−1.42994			−0.714969	+	0.699156i	$0.753559\pi$
$182$	−7.57187e13	−	7.94306e13i	−0.154433	−	0.162003i
$183$	9.67699e13			0.190462
$184$	9.89182e13	+	1.71331e14i	0.187914	+	0.325477i
$185$	1.36733e14	−	2.36828e14i	0.250759	−	0.434327i
$186$	2.93200e14	−	5.07837e14i	0.519194	−	0.899270i
$187$	−8.50890e13	−	1.47378e14i	−0.145513	−	0.252037i
$188$	3.30554e14			0.546030
$189$	4.32642e14	−	1.04903e14i	0.690441	−	0.167411i
$190$	−4.13674e13			−0.0637911
$191$	3.80180e14	+	6.58492e14i	0.566595	+	0.981372i	0.996899	+	0.0786877i	$0.0250730\pi$
$191$	3.80180e14	+	6.58492e14i	0.566595	+	0.981372i	−0.430304	+	0.902684i	$0.641594\pi$
$192$	−5.13234e13	+	8.88948e13i	−0.0739363	+	0.128061i
$193$	3.21102e12	−	5.56164e12i	0.00447219	−	0.00774605i	−0.863781	−	0.503868i	$-0.831910\pi$
$193$	3.21102e12	−	5.56164e12i	0.00447219	−	0.00774605i	0.868253	+	0.496122i	$0.165243\pi$
$194$	−2.49749e14	−	4.32578e14i	−0.336351	−	0.582577i
$195$	1.18128e14			0.153861
$196$	−1.89784e13	+	3.96403e14i	−0.0239109	+	0.499428i
$197$	4.19711e14			0.511588			0.255794	−	0.966731i	$-0.417663\pi$
$197$	4.19711e14			0.511588			0.255794	+	0.966731i	$0.417663\pi$
$198$	−8.73325e13	−	1.51264e14i	−0.103004	−	0.178407i
$199$	−7.53847e14	+	1.30570e15i	−0.860475	+	1.49039i	0.0109964	+	0.999940i	$0.496500\pi$
$199$	−7.53847e14	+	1.30570e15i	−0.860475	+	1.49039i	−0.871471	+	0.490447i	$0.836834\pi$
$200$	−1.32985e14	+	2.30337e14i	−0.146929	+	0.254489i
$201$	3.09517e14	+	5.36099e14i	0.331062	+	0.573417i
$202$	−8.42631e14			−0.872677
$203$	7.45228e14	−	1.80696e14i	0.747421	−	0.181227i
$204$	−2.42960e14			−0.236014
$205$	3.03705e14	+	5.26032e14i	0.285793	+	0.495008i
$206$	−5.66012e14	+	9.80361e14i	−0.516046	+	0.893818i
$207$	−2.40307e14	+	4.16225e14i	−0.212305	+	0.367723i
$208$	−4.62096e13	−	8.00373e13i	−0.0395658	−	0.0685300i
$209$	−1.92943e14			−0.160132
$210$	−2.94763e14	−	3.09212e14i	−0.237163	−	0.248789i
$211$	−9.49543e14			−0.740762			−0.370381	−	0.928880i	$-0.620773\pi$
$211$	−9.49543e14			−0.740762			−0.370381	+	0.928880i	$0.620773\pi$
$212$	4.52767e14	+	7.84215e14i	0.342525	+	0.593270i
$213$	4.76575e14	−	8.25452e14i	0.349674	−	0.605654i
$214$	−4.62771e14	+	8.01543e14i	−0.329364	+	0.570476i
$215$	5.33245e14	+	9.23607e14i	0.368194	+	0.637730i
$216$	3.74918e14			0.251181
$217$	5.38146e14	−	1.83194e15i	0.349874	−	1.19103i
$218$	1.01963e15			0.643392
$219$	−4.37654e14	−	7.58038e14i	−0.268067	−	0.464306i
$220$	1.26000e14	−	2.18238e14i	0.0749243	−	0.129773i
$221$	1.09376e14	−	1.89444e14i	0.0631496	−	0.109378i
$222$	−9.10485e14	−	1.57701e15i	−0.510479	−	0.884176i
$223$	6.07949e14			0.331044			0.165522	−	0.986206i	$-0.447069\pi$
$223$	6.07949e14			0.331044			0.165522	+	0.986206i	$0.447069\pi$
$224$	−9.42002e13	+	3.20674e14i	−0.0498241	+	0.169610i
$225$	−6.46137e14			−0.332000
$226$	1.55803e14	+	2.69859e14i	0.0777806	+	0.134720i
$227$	1.39309e15	−	2.41290e15i	0.675788	−	1.17050i	−0.300450	−	0.953798i	$-0.597137\pi$
$227$	1.39309e15	−	2.41290e15i	0.675788	−	1.17050i	0.976238	−	0.216702i	$-0.0695299\pi$
$228$	−1.37730e14	+	2.38556e14i	−0.0649311	+	0.112464i
$229$	−5.67556e14	−	9.83036e14i	−0.260063	−	0.450442i	0.706196	−	0.708017i	$-0.250410\pi$
$229$	−5.67556e14	−	9.83036e14i	−0.260063	−	0.450442i	−0.966258	+	0.257575i	$0.917077\pi$
$230$	−6.93412e14			−0.308859
$231$	−1.37481e15	−	1.44220e15i	−0.595339	−	0.624524i
$232$	6.45799e14			0.271910
$233$	1.01995e15	+	1.76660e15i	0.417604	+	0.723312i	0.995698	−	0.0926588i	$-0.0295366\pi$
$233$	1.01995e15	+	1.76660e15i	0.417604	+	0.723312i	−0.578094	+	0.815970i	$0.696203\pi$
$234$	1.12259e14	−	1.94439e14i	0.0447013	−	0.0774249i
$235$	−5.79292e14	+	1.00336e15i	−0.224366	+	0.388613i
$236$	−9.41629e14	−	1.63095e15i	−0.354774	−	0.614487i
$237$	3.67281e15			1.34628
$238$	−7.68812e14	+	1.86414e14i	−0.274202	+	0.0664857i
$239$	−3.57648e15			−1.24128			−0.620639	−	0.784096i	$-0.713127\pi$
$239$	−3.57648e15			−1.24128			−0.620639	+	0.784096i	$0.713127\pi$
$240$	−1.79888e14	−	3.11574e14i	−0.0607614	−	0.105242i
$241$	9.08192e14	−	1.57304e15i	0.298584	−	0.517163i	−0.677228	−	0.735773i	$-0.736819\pi$
$241$	9.08192e14	−	1.57304e15i	0.298584	−	0.517163i	0.975812	+	0.218610i	$0.0701522\pi$
$242$	−5.17048e14	+	8.95553e14i	−0.165474	+	0.286610i
$243$	1.21371e15	+	2.10220e15i	0.378158	+	0.654989i
$244$	2.65359e14			0.0805009
$245$	−1.16998e15	−	7.52300e14i	−0.345621	−	0.222234i
$246$	4.04466e15			1.16360
$247$	−1.24007e14	−	2.14786e14i	−0.0347468	−	0.0601833i
$248$	8.04003e14	−	1.39257e15i	0.219443	−	0.380087i
$249$	−2.48041e15	+	4.29619e15i	−0.659519	+	1.14232i
$250$	−1.02691e15	−	1.77866e15i	−0.266024	−	0.460767i
$251$	5.30330e15			1.33865			0.669325	−	0.742970i	$-0.266583\pi$
$251$	5.30330e15			1.33865			0.669325	+	0.742970i	$0.266583\pi$
$252$	−7.89083e14	+	1.91329e14i	−0.194097	+	0.0470628i
$253$	−3.23416e15			−0.775314
$254$	3.28873e13	+	5.69625e13i	0.00768439	+	0.0133098i
$255$	4.25784e14	−	7.37479e14i	0.0969791	−	0.167973i
$256$	−1.40737e14	+	2.43764e14i	−0.0312500	+	0.0541266i
$257$	1.07805e15	+	1.86724e15i	0.233385	+	0.404235i	0.958802	−	0.284074i	$-0.0916863\pi$
$257$	1.07805e15	+	1.86724e15i	0.233385	+	0.404235i	−0.725417	+	0.688310i	$0.758353\pi$
$258$	7.10161e15			1.49909
$259$	−4.09108e15	−	4.29164e15i	−0.842151	−	0.883435i
$260$	3.23927e14			0.0650310
$261$	7.84437e14	+	1.35869e15i	0.153601	+	0.266045i
$262$	−1.97562e15	+	3.42188e15i	−0.377351	+	0.653591i
$263$	−2.88067e15	+	4.98946e15i	−0.536761	+	0.929697i	0.462315	+	0.886716i	$0.347019\pi$
$263$	−2.88067e15	+	4.98946e15i	−0.536761	+	0.929697i	−0.999076	+	0.0429812i	$0.986314\pi$
$264$	−8.39017e14	−	1.45322e15i	−0.152526	−	0.264184i
$265$	−3.17388e15			−0.562979
$266$	−2.52793e14	+	8.60552e14i	−0.0437557	+	0.148952i
$267$	−4.15857e15			−0.702459
$268$	8.48748e14	+	1.47007e15i	0.139927	+	0.242361i
$269$	−4.23859e15	+	7.34146e15i	−0.682074	+	1.18139i	0.292272	+	0.956335i	$0.405589\pi$
$269$	−4.23859e15	+	7.34146e15i	−0.682074	+	1.18139i	−0.974347	+	0.225052i	$0.927745\pi$
$270$	−6.57040e14	+	1.13803e15i	−0.103211	+	0.178767i
$271$	4.24299e14	+	7.34908e14i	0.0650687	+	0.112702i	0.896724	−	0.442589i	$-0.145940\pi$
$271$	4.24299e14	+	7.34908e14i	0.0650687	+	0.112702i	−0.831656	+	0.555292i	$0.812607\pi$
$272$	−6.66236e14			−0.0997540
$273$	7.21871e14	−	2.45737e15i	0.105536	−	0.359264i
$274$	8.47055e15			1.20930
$275$	−2.17400e15	−	3.76547e15i	−0.303107	−	0.524997i
$276$	−2.30867e15	+	3.99873e15i	−0.314378	+	0.544519i
$277$	−3.47520e15	+	6.01923e15i	−0.462234	+	0.800613i	−0.999072	−	0.0430726i	$-0.986285\pi$
$277$	−3.47520e15	+	6.01923e15i	−0.462234	+	0.800613i	0.536838	+	0.843685i	$0.319619\pi$
$278$	−5.32109e15	−	9.21640e15i	−0.691368	−	1.19748i
$279$	3.90642e15			0.495851
$280$	−8.08289e14	−	8.47913e14i	−0.100240	−	0.105154i
$281$	−1.13665e15			−0.137732			−0.0688661	−	0.997626i	$-0.521938\pi$
$281$	−1.13665e15			−0.137732			−0.0688661	+	0.997626i	$0.521938\pi$
$282$	3.85743e15	+	6.68126e15i	0.456750	+	0.791115i
$283$	5.46610e15	−	9.46756e15i	0.632508	−	1.09554i	−0.354530	−	0.935045i	$-0.615359\pi$
$283$	5.46610e15	−	9.46756e15i	0.632508	−	1.09554i	0.987037	−	0.160491i	$-0.0513077\pi$
$284$	1.30685e15	−	2.26353e15i	0.147794	−	0.255986i
$285$	−4.82741e14	−	8.36133e14i	−0.0533609	−	0.0924237i
$286$	1.51083e15			0.163244
$287$	1.27988e16	−	3.10332e15i	1.35187	−	0.327789i
$288$	−6.83803e14			−0.0706122
$289$	4.16382e15	+	7.21194e15i	0.420393	+	0.728142i
$290$	−1.13176e15	+	1.96026e15i	−0.111729	+	0.193520i
$291$	5.82895e15	−	1.00960e16i	0.562711	−	0.974644i
$292$	−1.20012e15	−	2.07867e15i	−0.113302	−	0.196244i
$293$	−1.63957e15			−0.151388			−0.0756940	−	0.997131i	$-0.524117\pi$
$293$	−1.63957e15			−0.151388			−0.0756940	+	0.997131i	$0.524117\pi$
$294$	−8.23371e15	+	4.24227e15i	−0.743597	+	0.383125i
$295$	6.60078e15			0.583112
$296$	−2.49670e15	−	4.32442e15i	−0.215760	−	0.373707i
$297$	−3.06451e15	+	5.30789e15i	−0.259086	+	0.448751i
$298$	5.46868e15	−	9.47204e15i	0.452352	−	0.783497i
$299$	−2.07863e15	−	3.60030e15i	−0.168235	−	0.291391i
$300$	−6.20754e15			−0.491622
$301$	2.24721e16	−	5.44881e15i	1.74165	−	0.422298i
$302$	−1.72551e16			−1.30880
$303$	−9.83316e15	−	1.70315e16i	−0.729988	−	1.26438i
$304$	−3.77679e14	+	6.54160e14i	−0.0274438	+	0.0475341i
$305$	−4.65040e14	+	8.05472e14i	−0.0330781	+	0.0572930i
$306$	−8.09262e14	−	1.40168e15i	−0.0563508	−	0.0976024i
$307$	5.69931e15			0.388528			0.194264	−	0.980949i	$-0.437768\pi$
$307$	5.69931e15			0.388528			0.194264	+	0.980949i	$0.437768\pi$
$308$	−3.76996e15	−	3.95477e15i	−0.251627	−	0.263962i
$309$	−2.64205e16			−1.72668
$310$	2.81801e15	+	4.88094e15i	0.180340	+	0.312358i
$311$	4.65552e15	−	8.06360e15i	0.291760	−	0.505343i	−0.682466	−	0.730917i	$-0.739093\pi$
$311$	4.65552e15	−	8.06360e15i	0.291760	−	0.505343i	0.974226	+	0.225574i	$0.0724258\pi$
$312$	1.07849e15	−	1.86801e15i	0.0661931	−	0.114650i
$313$	2.82191e15	+	4.88770e15i	0.169631	+	0.293810i	0.938290	−	0.345849i	$-0.112409\pi$
$313$	2.82191e15	+	4.88770e15i	0.169631	+	0.293810i	−0.768659	+	0.639659i	$0.779076\pi$
$314$	3.39724e15			0.200024
$315$	8.02099e14	−	2.73049e15i	0.0462604	−	0.157479i
$316$	1.00715e16			0.569019
$317$	6.10586e15	+	1.05757e16i	0.337957	+	0.585359i	0.984048	−	0.177901i	$-0.0569308\pi$
$317$	6.10586e15	+	1.05757e16i	0.337957	+	0.585359i	−0.646091	+	0.763260i	$0.723597\pi$
$318$	−1.05672e16	+	1.83030e16i	−0.573039	+	0.992533i
$319$	−5.27864e15	+	9.14288e15i	−0.280468	+	0.485784i
$320$	−4.93282e14	−	8.54389e14i	−0.0256815	−	0.0444817i
$321$	−2.16014e16			−1.10204
$322$	−4.23738e15	+	1.44248e16i	−0.211853	+	0.721185i
$323$	−1.78789e15			−0.0876043
$324$	6.45454e15	+	1.11796e16i	0.309972	+	0.536887i
$325$	2.79451e15	−	4.84023e15i	0.131542	−	0.227837i
$326$	8.05906e15	−	1.39587e16i	0.371852	−	0.644066i
$327$	1.18987e16	+	2.06091e16i	0.538193	+	0.932178i
$328$	1.10911e16			0.491808
$329$	1.73326e16	+	1.81823e16i	0.753512	+	0.790451i
$330$	5.88147e15			0.250695
$331$	−6.64365e15	−	1.15071e16i	−0.277667	−	0.480934i	0.693137	−	0.720806i	$-0.256228\pi$
$331$	−6.64365e15	−	1.15071e16i	−0.277667	−	0.480934i	−0.970805	+	0.239872i	$0.922895\pi$
$332$	−6.80170e15	+	1.17809e16i	−0.278753	+	0.482815i
$333$	6.06538e15	−	1.05055e16i	0.243764	−	0.422212i
$334$	−1.66865e14	−	2.89018e14i	−0.00657676	−	0.0113913i
$335$	−5.94968e15			−0.229987
$336$	−7.58084e15	+	1.83813e15i	−0.287417	+	0.0696900i
$337$	2.83215e16			1.05323			0.526614	−	0.850105i	$-0.323461\pi$
$337$	2.83215e16			1.05323			0.526614	+	0.850105i	$0.323461\pi$
$338$	−8.72097e15	−	1.51052e16i	−0.318131	−	0.551019i
$339$	−3.63632e15	+	6.29829e15i	−0.130126	+	0.225385i
$340$	1.16757e15	−	2.02229e15i	0.0409893	−	0.0709956i
$341$	1.31436e16	+	2.27653e16i	0.452699	+	0.784098i
$342$	−1.83504e15			−0.0620118
$343$	−2.27995e16	+	1.97415e16i	−0.755985	+	0.654588i
$344$	1.94738e16			0.633609
$345$	−8.09184e15	−	1.40155e16i	−0.258359	−	0.447490i
$346$	8.42016e15	−	1.45841e16i	0.263831	−	0.456969i
$347$	−2.42080e16	+	4.19294e16i	−0.744417	+	1.28937i	0.206049	+	0.978542i	$0.433939\pi$
$347$	−2.42080e16	+	4.19294e16i	−0.744417	+	1.28937i	−0.950467	+	0.310827i	$0.899394\pi$
$348$	7.53621e15	+	1.30531e16i	0.227451	+	0.393957i
$349$	−3.92608e16			−1.16304			−0.581519	−	0.813533i	$-0.697541\pi$
$349$	−3.92608e16			−1.16304			−0.581519	+	0.813533i	$0.697541\pi$
$350$	−1.96429e16	+	4.76282e15i	−0.571167	+	0.138491i
$351$	−7.87840e15			−0.224875
$352$	−2.30073e15	−	3.98497e15i	−0.0644670	−	0.111660i
$353$	1.09539e16	−	1.89728e16i	0.301325	−	0.521909i	−0.675112	−	0.737716i	$-0.735905\pi$
$353$	1.09539e16	−	1.89728e16i	0.301325	−	0.521909i	0.976436	+	0.215806i	$0.0692379\pi$
$354$	2.19769e16	−	3.80650e16i	0.593532	−	1.02803i
$355$	4.58048e15	+	7.93362e15i	0.121458	+	0.210372i
$356$	−1.14035e16			−0.296902
$357$	−1.27396e16	−	1.33641e16i	−0.325696	−	0.341662i
$358$	2.31725e16			0.581746
$359$	−2.51750e16	−	4.36043e16i	−0.620662	−	1.07502i	−0.989363	−	0.145470i	$-0.953531\pi$
$359$	−2.51750e16	−	4.36043e16i	−0.620662	−	1.07502i	0.368701	−	0.929548i	$-0.379803\pi$
$360$	1.19836e15	−	2.07562e15i	0.0290148	−	0.0502552i
$361$	2.00130e16	−	3.46635e16i	0.475899	−	0.824281i
$362$	−2.16460e16	−	3.74920e16i	−0.505559	−	0.875655i
$363$	−2.41350e16			−0.553673
$364$	1.97949e15	−	6.73854e15i	0.0446061	−	0.151847i
$365$	8.41279e15			0.186224
$366$	3.09664e15	+	5.36353e15i	0.0673385	+	0.116634i
$367$	4.30705e16	−	7.46002e16i	0.920132	−	1.59372i	0.120923	−	0.992662i	$-0.461415\pi$
$367$	4.30705e16	−	7.46002e16i	0.920132	−	1.59372i	0.799209	−	0.601053i	$-0.205252\pi$
$368$	−6.33076e15	+	1.09652e16i	−0.132876	+	0.230147i
$369$	1.34722e16	+	2.33345e16i	0.277821	+	0.481201i
$370$	1.75018e16			0.354626
$371$	−1.93953e16	+	6.60250e16i	−0.386159	+	1.31455i
$372$	3.75296e16			0.734251
$373$	−1.65426e16	−	2.86526e16i	−0.318051	−	0.550880i	0.662030	−	0.749477i	$-0.269695\pi$
$373$	−1.65426e16	−	2.86526e16i	−0.318051	−	0.550880i	−0.980081	+	0.198597i	$0.936362\pi$
$374$	5.44569e15	−	9.43222e15i	0.102893	−	0.178217i
$375$	2.39672e16	−	4.15124e16i	0.445055	−	0.770858i
$376$	1.05777e16	+	1.83212e16i	0.193051	+	0.334373i
$377$	−1.35706e16			−0.243434
$378$	1.96588e16	+	2.06225e16i	0.346626	+	0.363618i
$379$	2.13699e16			0.370380			0.185190	−	0.982703i	$-0.440710\pi$
$379$	2.13699e16			0.370380			0.185190	+	0.982703i	$0.440710\pi$
$380$	−1.32376e15	−	2.29282e15i	−0.0225536	−	0.0390639i
$381$	−7.67564e14	+	1.32946e15i	−0.0128559	+	0.0222670i
$382$	−2.43315e16	+	4.21435e16i	−0.400643	+	0.693935i
$383$	1.11443e16	+	1.93025e16i	0.180410	+	0.312479i	0.942020	−	0.335556i	$-0.108924\pi$
$383$	1.11443e16	+	1.93025e16i	0.180410	+	0.312479i	−0.761610	+	0.648035i	$0.775591\pi$
$384$	−6.56940e15			−0.104562
$385$	1.86111e16	−	4.51264e15i	0.291258	−	0.0706214i
$386$	4.11010e14			0.00632463
$387$	2.36544e16	+	4.09706e16i	0.357924	+	0.619943i
$388$	1.59840e16	−	2.76850e16i	0.237836	−	0.411944i
$389$	1.09136e16	−	1.89028e16i	0.159696	−	0.276602i	−0.775063	−	0.631884i	$-0.782282\pi$
$389$	1.09136e16	−	1.89028e16i	0.159696	−	0.276602i	0.934759	+	0.355282i	$0.115615\pi$
$390$	3.78010e15	+	6.54732e15i	0.0543980	+	0.0942201i
$391$	−2.99691e16			−0.424156
$392$	−2.25782e16	+	1.16330e16i	−0.314290	+	0.161932i
$393$	−9.22188e16			−1.26261
$394$	1.34308e16	+	2.32628e16i	0.180874	+	0.313282i
$395$	−1.76502e16	+	3.05710e16i	−0.233812	+	0.404975i
$396$	5.58928e15	−	9.68092e15i	0.0728345	−	0.126153i
$397$	−1.31629e16	−	2.27988e16i	−0.168738	−	0.292263i	0.769238	−	0.638962i	$-0.220636\pi$
$397$	−1.31629e16	−	2.27988e16i	−0.168738	−	0.292263i	−0.937977	+	0.346699i	$0.887303\pi$
$398$	−9.64924e16			−1.21690
$399$	−2.03438e16	+	4.93276e15i	−0.252410	+	0.0612020i
$400$	−1.70221e16			−0.207789
$401$	8.00434e16	+	1.38639e17i	0.961362	+	1.66513i	0.719086	+	0.694921i	$0.244561\pi$
$401$	8.00434e16	+	1.38639e17i	0.961362	+	1.66513i	0.242276	+	0.970207i	$0.422106\pi$
$402$	−1.98091e16	+	3.43103e16i	−0.234097	+	0.405467i
$403$	−1.68951e16	+	2.92631e16i	−0.196461	+	0.340281i
$404$	−2.69642e16	−	4.67033e16i	−0.308538	−	0.534403i
$405$	−4.52460e16			−0.509475
$406$	3.38625e16	+	3.55225e16i	0.375232	+	0.393626i
$407$	8.16304e16			0.890202
$408$	−7.77470e15	−	1.34662e16i	−0.0834436	−	0.144528i
$409$	−9.81791e15	+	1.70051e16i	−0.103709	+	0.179630i	−0.913210	−	0.407489i	$-0.866404\pi$
$409$	−9.81791e15	+	1.70051e16i	−0.103709	+	0.179630i	0.809501	+	0.587119i	$0.199738\pi$
$410$	−1.94371e16	+	3.36660e16i	−0.202086	+	0.350023i
$411$	9.88478e16	+	1.71209e17i	1.01157	+	1.75209i
$412$	−7.24495e16			−0.729799
$413$	4.03368e16	−	1.37314e17i	0.399969	−	1.36156i
$414$	−3.07593e16			−0.300244
$415$	−2.38398e16	−	4.12917e16i	−0.229081	−	0.396781i
$416$	2.95741e15	−	5.12239e15i	0.0279773	−	0.0484580i
$417$	1.24190e17	−	2.15103e17i	1.15665	−	2.00338i
$418$	−6.17417e15	−	1.06940e16i	−0.0566151	−	0.0980603i
$419$	1.22382e17			1.10491			0.552454	−	0.833544i	$-0.313692\pi$
$419$	1.22382e17			1.10491			0.552454	+	0.833544i	$0.313692\pi$
$420$	7.70589e15	−	2.62322e16i	0.0685019	−	0.233192i
$421$	−2.43087e16			−0.212778			−0.106389	−	0.994325i	$-0.533929\pi$
$421$	−2.43087e16			−0.212778			−0.106389	+	0.994325i	$0.533929\pi$
$422$	−3.03854e16	−	5.26290e16i	−0.261899	−	0.453622i
$423$	−2.56971e16	+	4.45086e16i	−0.218108	+	0.377774i
$424$	−2.89771e16	+	5.01898e16i	−0.242201	+	0.419505i
$425$	−2.01452e16	−	3.48925e16i	−0.165823	−	0.287213i
$426$	6.10016e16			0.494514
$427$	1.39141e16	+	1.45962e16i	0.111090	+	0.116536i
$428$	−5.92347e16			−0.465791
$429$	1.76308e16	+	3.05375e16i	0.136553	+	0.236516i
$430$	−3.41277e16	+	5.91108e16i	−0.260352	+	0.450943i
$431$	−6.14438e16	+	1.06424e17i	−0.461717	+	0.799717i	−0.999047	−	0.0436554i	$-0.986100\pi$
$431$	−6.14438e16	+	1.06424e17i	−0.461717	+	0.799717i	0.537330	+	0.843372i	$0.319433\pi$
$432$	1.19974e16	+	2.07801e16i	0.0888059	+	0.153816i
$433$	−1.41055e17			−1.02853			−0.514267	−	0.857630i	$-0.671936\pi$
$433$	−1.41055e17			−1.02853			−0.514267	+	0.857630i	$0.671936\pi$
$434$	1.18757e17	−	2.87951e16i	0.853054	−	0.206840i
$435$	−5.28285e16			−0.373842
$436$	3.26282e16	+	5.65136e16i	0.227473	+	0.393995i
$437$	−1.69891e16	+	2.94259e16i	−0.116692	+	0.202116i
$438$	2.80098e16	−	4.85145e16i	0.189552	−	0.328314i
$439$	−7.34941e16	−	1.27296e17i	−0.490042	−	0.848777i	0.509893	−	0.860238i	$-0.329685\pi$
$439$	−7.34941e16	−	1.27296e17i	−0.490042	−	0.848777i	−0.999934	+	0.0114609i	$0.996352\pi$
$440$	1.61280e16			0.105959
$441$	−5.18998e16	−	3.33716e16i	−0.335981	−	0.216036i
$442$	1.40001e16			0.0893070
$443$	−9.34433e16	−	1.61849e17i	−0.587386	−	1.01738i	−0.994573	−	0.104038i	$-0.966824\pi$
$443$	−9.34433e16	−	1.61849e17i	−0.587386	−	1.01738i	0.407187	−	0.913345i	$-0.366510\pi$
$444$	5.82710e16	−	1.00928e17i	0.360964	−	0.625207i
$445$	1.99845e16	−	3.46142e16i	0.121998	−	0.211307i
$446$	1.94544e16	+	3.36959e16i	0.117042	+	0.202722i
$447$	2.55269e17			1.51356
$448$	−2.07880e16	+	5.04046e15i	−0.121480	+	0.0294553i
$449$	2.15477e17			1.24108			0.620540	−	0.784175i	$-0.286913\pi$
$449$	2.15477e17			1.24108			0.620540	+	0.784175i	$0.286913\pi$
$450$	−2.06764e16	−	3.58125e16i	−0.117380	−	0.203308i
$451$	−9.06570e16	+	1.57022e17i	−0.507287	+	0.878647i
$452$	−9.97141e15	+	1.72710e16i	−0.0549992	+	0.0952614i
$453$	−2.01360e17	−	3.48765e17i	−1.09480	−	1.89625i
$454$	1.78315e17			0.955709
$455$	1.69851e16	+	1.78178e16i	0.0897418	+	0.0941411i
$456$	−1.76295e16			−0.0918264
$457$	1.91954e16	+	3.32474e16i	0.0985694	+	0.170727i	0.911093	−	0.412201i	$-0.135240\pi$
$457$	1.91954e16	+	3.32474e16i	0.0985694	+	0.170727i	−0.812523	+	0.582929i	$0.801907\pi$
$458$	3.63236e16	−	6.29143e16i	0.183892	−	0.318510i
$459$	−2.83971e16	+	4.91853e16i	−0.141740	+	0.245501i
$460$	−2.21892e16	−	3.84328e16i	−0.109198	−	0.189137i
$461$	3.15284e17			1.52984			0.764921	−	0.644124i	$-0.222778\pi$
$461$	3.15284e17			1.52984			0.764921	+	0.644124i	$0.222778\pi$
$462$	3.59412e16	−	1.22350e17i	0.171957	−	0.585372i
$463$	−2.28642e17			−1.07865			−0.539323	−	0.842099i	$-0.681320\pi$
$463$	−2.28642e17			−1.07865			−0.539323	+	0.842099i	$0.681320\pi$
$464$	2.06656e16	+	3.57938e16i	0.0961347	+	0.166510i
$465$	−6.57702e16	+	1.13917e17i	−0.301707	+	0.522571i
$466$	−6.52767e16	+	1.13063e17i	−0.295291	+	0.511458i
$467$	−1.06511e17	−	1.84482e17i	−0.475153	−	0.822989i	0.524442	−	0.851446i	$-0.324274\pi$
$467$	−1.06511e17	−	1.84482e17i	−0.475153	−	0.822989i	−0.999595	+	0.0284570i	$0.990941\pi$
$468$	1.43692e16			0.0632171
$469$	−3.63580e16	+	1.23769e17i	−0.157753	+	0.537018i
$470$	−7.41494e16			−0.317301
$471$	3.96444e16	+	6.86661e16i	0.167319	+	0.289805i
$472$	6.02643e16	−	1.04381e17i	0.250863	−	0.434508i
$473$	−1.59175e17	+	2.75700e17i	−0.653550	+	1.13198i
$474$	1.17530e17	+	2.03568e17i	0.475981	+	0.824424i
$475$	−4.56801e16			−0.182481
$476$	−3.49341e16	−	3.66466e16i	−0.137659	−	0.144407i
$477$	−1.40791e17			−0.547276
$478$	−1.14447e17	−	1.98228e17i	−0.438858	−	0.760124i
$479$	−1.57833e16	+	2.73374e16i	−0.0597058	+	0.103413i	−0.894333	−	0.447401i	$-0.852350\pi$
$479$	−1.57833e16	+	2.73374e16i	−0.0597058	+	0.103413i	0.834628	+	0.550815i	$0.185683\pi$
$480$	1.15128e16	−	1.99408e16i	0.0429648	−	0.0744172i
$481$	5.24649e16	+	9.08719e16i	0.193164	+	0.334570i
$482$	1.16249e17			0.422262
$483$	−3.41007e17	+	8.26841e16i	−1.22210	+	0.296323i
$484$	−6.61821e16			−0.234016
$485$	5.60234e16	+	9.70354e16i	0.195456	+	0.338539i
$486$	−7.76773e16	+	1.34541e17i	−0.267398	+	0.463147i
$487$	−2.71494e17	+	4.70241e17i	−0.922193	+	1.59729i	−0.126179	+	0.992008i	$0.540271\pi$
$487$	−2.71494e17	+	4.70241e17i	−0.922193	+	1.59729i	−0.796014	+	0.605278i	$0.793062\pi$
$488$	8.49150e15	+	1.47077e16i	0.0284614	+	0.0492965i
$489$	3.76184e17			1.24421
$490$	4.25721e15	−	8.89207e16i	0.0138948	−	0.290221i
$491$	2.87085e17			0.924658			0.462329	−	0.886708i	$-0.347014\pi$
$491$	2.87085e17			0.924658			0.462329	+	0.886708i	$0.347014\pi$
$492$	1.29429e17	+	2.24178e17i	0.411395	+	0.712556i
$493$	−4.89143e16	+	8.47220e16i	−0.153437	+	0.265761i
$494$	7.93643e15	−	1.37463e16i	0.0245697	−	0.0425560i
$495$	1.95903e16	+	3.39314e16i	0.0598560	+	0.103674i
$496$	1.02912e17			0.310339
$497$	1.93031e17	−	4.68043e16i	0.574528	−	0.139306i
$498$	−3.17492e17			−0.932701
$499$	−2.64712e15	−	4.58495e15i	−0.00767575	−	0.0132948i	0.862162	−	0.506633i	$-0.169110\pi$
$499$	−2.64712e15	−	4.58495e15i	−0.00767575	−	0.0132948i	−0.869838	+	0.493338i	$0.835777\pi$
$500$	6.57221e16	−	1.13834e17i	0.188108	−	0.325812i
$501$	3.89449e15	−	6.74545e15i	0.0110028	−	0.0190575i
$502$	1.69706e17	+	2.93939e17i	0.473284	+	0.819753i
$503$	9.65557e16			0.265819			0.132909	−	0.991128i	$-0.457568\pi$
$503$	9.65557e16			0.265819			0.132909	+	0.991128i	$0.457568\pi$
$504$	−3.58552e16	−	3.76129e16i	−0.0974437	−	0.102221i
$505$	1.89018e17			0.507118
$506$	−1.03493e17	−	1.79255e17i	−0.274115	−	0.474781i
$507$	2.03540e17	−	3.52542e17i	0.532229	−	0.921848i
$508$	−2.10479e15	+	3.64560e15i	−0.00543369	+	0.00941142i
$509$	−2.70435e17	−	4.68407e17i	−0.689283	−	1.19387i	−0.972070	−	0.234691i	$-0.924592\pi$
$509$	−2.70435e17	−	4.68407e17i	−0.689283	−	1.19387i	0.282787	−	0.959183i	$-0.408741\pi$
$510$	5.45003e16			0.137149
$511$	5.14099e16	−	1.75008e17i	0.127735	−	0.434833i
$512$	−1.80144e16			−0.0441942
$513$	3.21958e16	+	5.57648e16i	0.0779896	+	0.135082i
$514$	−6.89952e16	+	1.19503e17i	−0.165028	+	0.285838i
$515$	1.26967e17	−	2.19913e17i	0.299877	−	0.519403i
$516$	2.27252e17	+	3.93611e17i	0.530010	+	0.918004i
$517$	−3.45842e17			−0.796506
$518$	1.06952e17	−	3.64083e17i	0.243246	−	0.828051i
$519$	3.93040e17			0.882772
$520$	1.03657e16	+	1.79539e16i	0.0229919	+	0.0398232i
$521$	−6.51595e16	+	1.12860e17i	−0.142736	+	0.247225i	−0.928526	−	0.371268i	$-0.878923\pi$
$521$	−6.51595e16	+	1.12860e17i	−0.142736	+	0.247225i	0.785790	+	0.618493i	$0.212257\pi$
$522$	−5.02040e16	+	8.69559e16i	−0.108613	+	0.188122i
$523$	−4.34304e17	−	7.52237e17i	−0.927969	−	1.60729i	−0.786716	−	0.617315i	$-0.788220\pi$
$523$	−4.34304e17	−	7.52237e17i	−0.927969	−	1.60729i	−0.141253	−	0.989974i	$-0.545113\pi$
$524$	−2.52879e17			−0.533654
$525$	−3.25492e17	−	3.41449e17i	−0.678430	−	0.711688i
$526$	−3.68725e17			−0.759094
$527$	1.21794e17	+	2.10954e17i	0.247661	+	0.428961i
$528$	5.36971e16	−	9.30061e16i	0.107853	−	0.186806i
$529$	−3.27570e16	+	5.67368e16i	−0.0649894	+	0.112565i
$530$	−1.01564e17	−	1.75914e17i	−0.199043	−	0.344753i
$531$	2.92807e17			0.566848
$532$	−5.57860e16	+	1.35264e16i	−0.106684	+	0.0258677i
$533$	−2.33065e17			−0.440302
$534$	−1.33074e17	−	2.30491e17i	−0.248357	−	0.430166i
$535$	1.03808e17	−	1.79801e17i	0.191396	−	0.331507i
$536$	−5.43198e16	+	9.40847e16i	−0.0989435	+	0.171375i
$537$	2.70414e17	+	4.68370e17i	0.486627	+	0.842862i
$538$	−5.42540e17			−0.964599
$539$	1.98562e16	−	4.14737e17i	0.0348793	−	0.728527i
$540$	−8.41011e16			−0.145963
$541$	2.99150e17	+	5.18143e17i	0.512988	+	0.888520i	0.999887	+	0.0150622i	$0.00479462\pi$
$541$	2.99150e17	+	5.18143e17i	0.512988	+	0.888520i	−0.486899	+	0.873458i	$0.661872\pi$
$542$	−2.71552e16	+	4.70341e16i	−0.0460105	+	0.0796925i
$543$	5.05200e17	−	8.75033e17i	0.845794	−	1.46496i
$544$	−2.13196e16	−	3.69265e16i	−0.0352684	−	0.0610866i
$545$	−2.28722e17			−0.373879
$546$	1.59301e17	−	3.86258e16i	0.257316	−	0.0623916i
$547$	6.94479e17			1.10851			0.554257	−	0.832345i	$-0.313002\pi$
$547$	6.94479e17			1.10851			0.554257	+	0.832345i	$0.313002\pi$
$548$	2.71057e17	+	4.69485e17i	0.427551	+	0.740540i
$549$	−2.06289e16	+	3.57303e16i	−0.0321555	+	0.0556950i
$550$	1.39136e17	−	2.40990e17i	0.214329	−	0.371229i
$551$	5.54576e16	+	9.60553e16i	0.0844258	+	0.146230i
$552$	−2.95510e17			−0.444598
$553$	5.28098e17	+	5.53987e17i	0.785238	+	0.823732i
$554$	−4.44826e17			−0.653698
$555$	2.04239e17	+	3.53752e17i	0.296643	+	0.513800i
$556$	3.40550e17	−	5.89849e17i	0.488871	−	0.846750i
$557$	−4.32451e17	+	7.49027e17i	−0.613590	+	1.06277i	0.377040	+	0.926197i	$0.376942\pi$
$557$	−4.32451e17	+	7.49027e17i	−0.613590	+	1.06277i	−0.990630	+	0.136572i	$0.956391\pi$
$558$	1.25005e17	+	2.16516e17i	0.175310	+	0.303646i
$559$	−4.09216e17			−0.567252
$560$	2.11309e16	−	7.19331e16i	0.0289531	−	0.0985614i
$561$	2.54196e17			0.344279
$562$	−3.63728e16	−	6.29995e16i	−0.0486957	−	0.0843434i
$563$	−6.04730e16	+	1.04742e17i	−0.0800307	+	0.138617i	−0.903263	−	0.429088i	$-0.858835\pi$
$563$	−6.04730e16	+	1.04742e17i	−0.0800307	+	0.138617i	0.823232	+	0.567705i	$0.192169\pi$
$564$	−2.46875e17	+	4.27601e17i	−0.322971	+	0.559403i
$565$	−3.49496e16	−	6.05344e16i	−0.0451988	−	0.0782866i
$566$	6.99661e17			0.894501
$567$	−2.76495e17	+	9.41237e17i	−0.349460	+	1.18962i
$568$	1.67277e17			0.209012
$569$	3.13843e17	+	5.43592e17i	0.387688	+	0.671496i	0.992138	−	0.125147i	$-0.0399404\pi$
$569$	3.13843e17	+	5.43592e17i	0.387688	+	0.671496i	−0.604450	+	0.796643i	$0.706607\pi$
$570$	3.08954e16	−	5.35125e16i	0.0377318	−	0.0653535i
$571$	6.18567e17	−	1.07139e18i	0.746882	−	1.29364i	−0.202428	−	0.979297i	$-0.564883\pi$
$571$	6.18567e17	−	1.07139e18i	0.746882	−	1.29364i	0.949310	−	0.314340i	$-0.101783\pi$
$572$	4.83467e16	+	8.37390e16i	0.0577155	+	0.0999662i
$573$	−1.13576e18			−1.34054
$574$	5.81564e17	+	6.10073e17i	0.678688	+	0.711959i
$575$	−7.65702e17			−0.883525
$576$	−2.18817e16	−	3.79002e16i	−0.0249652	−	0.0432410i
$577$	−4.22370e17	+	7.31566e17i	−0.476486	+	0.825298i	−0.999637	−	0.0269418i	$-0.991423\pi$
$577$	−4.22370e17	+	7.31566e17i	−0.476486	+	0.825298i	0.523151	+	0.852240i	$0.324756\pi$
$578$	−2.66484e17	+	4.61564e17i	−0.297263	+	0.514874i
$579$	4.79632e15	+	8.30747e15i	0.00529051	+	0.00916343i
$580$	−1.44865e17			−0.158009
$581$	−1.00466e18	+	2.43600e17i	−1.08361	+	0.262744i
$582$	7.46105e17			0.795794
$583$	−4.73707e17	−	8.20485e17i	−0.499648	−	0.865416i
$584$	7.68077e16	−	1.33035e17i	0.0801164	−	0.138766i
$585$	−2.51819e16	+	4.36163e16i	−0.0259762	+	0.0449920i
$586$	−5.24663e16	−	9.08744e16i	−0.0535237	−	0.0927058i
$587$	−9.19950e17			−0.928146			−0.464073	−	0.885797i	$-0.653613\pi$
$587$	−9.19950e17			−0.928146			−0.464073	+	0.885797i	$0.653613\pi$
$588$	−4.98609e17	−	3.20606e17i	−0.497516	−	0.319903i
$589$	2.76173e17			0.272541
$590$	2.11225e17	+	3.65852e17i	0.206161	+	0.357082i
$591$	−3.13463e17	+	5.42934e17i	−0.302599	+	0.524117i
$592$	1.59789e17	−	2.76763e17i	0.152565	−	0.264251i
$593$	3.65725e16	+	6.33454e16i	0.0345381	+	0.0598218i	0.882778	−	0.469791i	$-0.155671\pi$
$593$	3.65725e16	+	6.33454e16i	0.0345381	+	0.0598218i	−0.848240	+	0.529613i	$0.822337\pi$
$594$	−3.92258e17			−0.366403
$595$	1.72459e17	−	4.18161e16i	0.159340	−	0.0386352i
$596$	6.99991e17			0.639723
$597$	−1.12603e18	−	1.95034e18i	−1.01792	−	1.76310i
$598$	1.33033e17	−	2.30419e17i	0.118960	−	0.206044i
$599$	1.99308e17	−	3.45212e17i	0.176299	−	0.305360i	−0.764311	−	0.644848i	$-0.776921\pi$
$599$	1.99308e17	−	3.45212e17i	0.176299	−	0.305360i	0.940610	+	0.339489i	$0.110254\pi$
$600$	−1.98641e17	−	3.44057e17i	−0.173815	−	0.301056i
$601$	2.02331e18			1.75137			0.875686	−	0.482882i	$-0.160410\pi$
$601$	2.02331e18			1.75137			0.875686	+	0.482882i	$0.160410\pi$
$602$	1.02111e18	+	1.07117e18i	0.874370	+	0.917233i
$603$	−2.63924e17			−0.223572
$604$	−5.52162e17	−	9.56373e17i	−0.462729	−	0.801470i
$605$	1.15983e17	−	2.00889e17i	0.0961582	−	0.166551i
$606$	6.29322e17	−	1.09002e18i	0.516180	−	0.894049i
$607$	9.11136e17	+	1.57813e18i	0.739361	+	1.28061i	0.952783	+	0.303651i	$0.0982057\pi$
$607$	9.11136e17	+	1.57813e18i	0.739361	+	1.28061i	−0.213422	+	0.976960i	$0.568461\pi$
$608$	−4.83430e16			−0.0388115
$609$	−3.22831e17	+	1.09897e18i	−0.256426	+	0.872920i
$610$	−5.95251e16			−0.0467795
$611$	−2.22277e17	−	3.84995e17i	−0.172833	−	0.299355i
$612$	5.17928e16	−	8.97077e16i	0.0398460	−	0.0690153i
$613$	8.93380e17	−	1.54738e18i	0.680054	−	1.17789i	−0.294910	−	0.955525i	$-0.595290\pi$
$613$	8.93380e17	−	1.54738e18i	0.680054	−	1.17789i	0.974964	−	0.222363i	$-0.0713769\pi$
$614$	1.82378e17	+	3.15888e17i	0.137366	+	0.237924i
$615$	−9.07292e17			−0.676175
$616$	9.85569e16	−	3.35505e17i	0.0726795	−	0.247414i
$617$	8.80000e17			0.642139			0.321070	−	0.947056i	$-0.395958\pi$
$617$	8.80000e17			0.642139			0.321070	+	0.947056i	$0.395958\pi$
$618$	−8.45456e17	−	1.46437e18i	−0.610472	−	1.05737i
$619$	4.84990e16	−	8.40027e16i	0.0346532	−	0.0600211i	−0.848179	−	0.529710i	$-0.822301\pi$
$619$	4.84990e16	−	8.40027e16i	0.0346532	−	0.0600211i	0.882832	+	0.469689i	$0.155634\pi$
$620$	−1.80353e17	+	3.12380e17i	−0.127520	+	0.220871i
$621$	5.39675e17	+	9.34745e17i	0.377604	+	0.654030i
$622$	5.95906e17			0.412611
$623$	−5.97943e17	−	6.27255e17i	−0.409720	−	0.429805i
$624$	1.38047e17			0.0936112
$625$	−3.88906e17	−	6.73606e17i	−0.260991	−	0.452049i
$626$	−1.80602e17	+	3.12813e17i	−0.119947	+	0.207755i
$627$	1.44100e17	−	2.49589e17i	0.0947164	−	0.164054i
$628$	1.08712e17	+	1.88294e17i	0.0707193	+	0.122489i
$629$	7.56424e17			0.487008
$630$	1.77006e17	−	4.29187e16i	0.112791	−	0.0273485i
$631$	−8.85605e15			−0.00558533			−0.00279267	−	0.999996i	$-0.500889\pi$
$631$	−8.85605e15			−0.00558533			−0.00279267	+	0.999996i	$0.500889\pi$
$632$	3.22287e17	+	5.58218e17i	0.201179	+	0.348452i
$633$	7.09170e17	−	1.22832e18i	0.438153	−	0.758904i
$634$	−3.90775e17	+	6.76842e17i	−0.238972	+	0.413911i
$635$	−7.37724e15	−	1.27778e16i	−0.00446545	−	0.00773438i
$636$	−1.35260e18			−0.810400
$637$	4.74451e17	−	2.44452e17i	0.281375	−	0.144973i
$638$	−6.75666e17			−0.396641
$639$	2.03187e17	+	3.51931e17i	0.118070	+	0.204504i
$640$	3.15700e16	−	5.46809e16i	0.0181596	−	0.0314533i
$641$	−3.07694e17	+	5.32941e17i	−0.175203	+	0.303460i	−0.940232	−	0.340536i	$-0.889392\pi$
$641$	−3.07694e17	+	5.32941e17i	−0.175203	+	0.303460i	0.765029	+	0.643996i	$0.222725\pi$
$642$	−6.91244e17	−	1.19727e18i	−0.389631	−	0.674861i
$643$	−9.48803e17			−0.529425			−0.264713	−	0.964327i	$-0.585277\pi$
$643$	−9.48803e17			−0.529425			−0.264713	+	0.964327i	$0.585277\pi$
$644$	−9.35100e17	+	2.26734e17i	−0.516535	+	0.125244i
$645$	−1.59302e18			−0.871132
$646$	−5.72126e16	−	9.90951e16i	−0.0309728	−	0.0536464i
$647$	−9.09981e16	+	1.57613e17i	−0.0487702	+	0.0844725i	−0.889380	−	0.457169i	$-0.848864\pi$
$647$	−9.09981e16	+	1.57613e17i	−0.0487702	+	0.0844725i	0.840610	+	0.541641i	$0.182197\pi$
$648$	−4.13090e17	+	7.15494e17i	−0.219183	+	0.379637i
$649$	9.85178e17	+	1.70638e18i	0.517517	+	0.896365i
$650$	3.57697e17			0.186028
$651$	1.96786e18	+	2.06433e18i	1.01325	+	1.06293i
$652$	1.03156e18			0.525878
$653$	−1.38478e18	−	2.39851e18i	−0.698947	−	1.21061i	−0.968832	−	0.247720i	$-0.920319\pi$
$653$	−1.38478e18	−	2.39851e18i	−0.698947	−	1.21061i	0.269884	−	0.962893i	$-0.413015\pi$
$654$	−7.61515e17	+	1.31898e18i	−0.380560	+	0.659149i
$655$	4.43169e17	−	7.67590e17i	0.219281	−	0.379805i
$656$	3.54916e17	+	6.14733e17i	0.173881	+	0.301170i
$657$	3.73186e17			0.181030
$658$	−4.53121e17	+	1.54250e18i	−0.217644	+	0.740897i
$659$	−1.98995e18			−0.946427			−0.473213	−	0.880948i	$-0.656906\pi$
$659$	−1.98995e18			−0.946427			−0.473213	+	0.880948i	$0.656906\pi$
$660$	1.88207e17	+	3.25984e17i	0.0886340	+	0.153519i
$661$	5.81844e17	−	1.00778e18i	0.271330	−	0.469957i	−0.697873	−	0.716222i	$-0.745870\pi$
$661$	5.81844e17	−	1.00778e18i	0.271330	−	0.469957i	0.969203	+	0.246265i	$0.0792033\pi$
$662$	4.25194e17	−	7.36457e17i	0.196340	−	0.340072i
$663$	1.63375e17	+	2.82974e17i	0.0747047	+	0.129392i
$664$	−8.70617e17			−0.394216
$665$	5.67062e16	−	1.93038e17i	0.0254267	−	0.0865569i
$666$	7.76368e17			0.344735
$667$	9.29594e17	+	1.61010e18i	0.408767	+	0.708005i
$668$	1.06793e16	−	1.84972e16i	0.00465047	−	0.00805486i
$669$	−4.54049e17	+	7.86436e17i	−0.195809	+	0.339151i
$670$	−1.90390e17	−	3.29765e17i	−0.0813126	−	0.140837i
$671$	−2.77632e17			−0.117428
$672$	−3.44467e17	−	3.61353e17i	−0.144293	−	0.151367i
$673$	1.44542e18			0.599650			0.299825	−	0.953994i	$-0.403072\pi$
$673$	1.44542e18			0.599650			0.299825	+	0.953994i	$0.403072\pi$
$674$	9.06289e17	+	1.56974e18i	0.372372	+	0.644967i
$675$	−7.25538e17	+	1.25667e18i	−0.295247	+	0.511383i
$676$	5.58142e17	−	9.66731e17i	0.224953	−	0.389630i
$677$	−1.90818e18	−	3.30507e18i	−0.761716	−	1.31933i	−0.941965	−	0.335710i	$-0.891024\pi$
$677$	−1.90818e18	−	3.30507e18i	−0.761716	−	1.31933i	0.180249	−	0.983621i	$-0.442310\pi$
$678$	−4.65449e17			−0.184026
$679$	2.36095e18	−	5.72459e17i	0.924555	−	0.224177i
$680$	1.49449e17			0.0579676
$681$	2.08087e18	+	3.60417e18i	0.799444	+	1.38468i
$682$	−8.41188e17	+	1.45698e18i	−0.320107	+	0.554441i
$683$	−1.14349e17	+	1.98058e17i	−0.0431019	+	0.0746547i	−0.886772	−	0.462208i	$-0.847057\pi$
$683$	−1.14349e17	+	1.98058e17i	−0.0431019	+	0.0746547i	0.843670	+	0.536863i	$0.180391\pi$
$684$	−5.87211e16	−	1.01708e17i	−0.0219245	−	0.0379743i
$685$	−1.90010e18			−0.702729
$686$	−1.82377e18	−	6.31948e17i	−0.668133	−	0.231513i
$687$	1.69553e18			0.615298
$688$	6.23162e17	+	1.07935e18i	0.224015	+	0.388005i
$689$	6.08915e17	−	1.05467e18i	0.216836	−	0.375571i
$690$	5.17878e17	−	8.96990e17i	0.182687	−	0.316423i
$691$	1.65297e18	+	2.86303e18i	0.577642	+	1.00051i	0.995749	+	0.0921074i	$0.0293603\pi$
$691$	1.65297e18	+	2.86303e18i	0.577642	+	1.00051i	−0.418107	+	0.908398i	$0.637306\pi$
$692$	1.07778e18			0.373113
$693$	8.25578e17	−	2.00178e17i	0.283134	−	0.0686516i
$694$	−3.09862e18			−1.05276
$695$	1.19362e18	+	2.06741e18i	0.401758	+	0.695866i
$696$	−4.82317e17	+	8.35398e17i	−0.160832	+	0.278569i
$697$	−8.40068e17	+	1.45504e18i	−0.277524	+	0.480686i
$698$	−1.25634e18	−	2.17605e18i	−0.411196	−	0.712212i
$699$	−3.04701e18			−0.988035
$700$	−8.92555e17	−	9.36310e17i	−0.286746	−	0.300803i
$701$	−1.97078e18			−0.627293			−0.313647	−	0.949540i	$-0.601551\pi$
$701$	−1.97078e18			−0.627293			−0.313647	+	0.949540i	$0.601551\pi$
$702$	−2.52109e17	−	4.36666e17i	−0.0795055	−	0.137708i
$703$	4.28805e17	−	7.42713e17i	0.133983	−	0.232066i
$704$	1.47246e17	−	2.55038e17i	0.0455851	−	0.0789557i
$705$	−8.65293e17	−	1.49873e18i	−0.265420	−	0.459721i
$706$	1.40210e18			0.426137
$707$	1.15507e18	−	3.93207e18i	0.347843	−	1.18412i
$708$	2.81304e18			0.839381
$709$	−1.90872e18	−	3.30601e18i	−0.564342	−	0.977470i	−0.997111	−	0.0759644i	$-0.975796\pi$
$709$	−1.90872e18	−	3.30601e18i	−0.564342	−	0.977470i	0.432768	−	0.901505i	$-0.357537\pi$
$710$	−2.93151e17	+	5.07752e17i	−0.0858839	+	0.148755i
$711$	−7.82950e17	+	1.35611e18i	−0.227291	+	0.393679i
$712$	−3.64912e17	−	6.32046e17i	−0.104971	−	0.181815i
$713$	4.62929e18			1.31957
$714$	3.33047e17	−	1.13375e18i	0.0940735	−	0.320243i
$715$	−3.38908e17			−0.0948622
$716$	7.41520e17	+	1.28435e18i	0.205678	+	0.356245i
$717$	2.67111e18	−	4.62649e18i	0.734204	−	1.27168i
$718$	1.61120e18	−	2.79068e18i	0.438874	−	0.760152i
$719$	−1.80548e18	−	3.12718e18i	−0.487365	−	0.844141i	0.512529	−	0.858670i	$-0.328709\pi$
$719$	−1.80548e18	−	3.12718e18i	−0.487365	−	0.844141i	−0.999894	+	0.0145287i	$0.995375\pi$
$720$	1.53390e17			0.0410332
$721$	−3.79889e18	−	3.98512e18i	−1.00711	−	1.05648i
$722$	2.56166e18			0.673022
$723$	1.35657e18	+	2.34966e18i	0.353219	+	0.611794i
$724$	1.38534e18	−	2.39949e18i	0.357484	−	0.619181i
$725$	−1.24974e18	+	2.16462e18i	−0.319613	+	0.553585i
$726$	−7.72319e17	−	1.33769e18i	−0.195753	−	0.339054i
$727$	−3.60755e18			−0.906230			−0.453115	−	0.891452i	$-0.649687\pi$
$727$	−3.60755e18			−0.906230			−0.453115	+	0.891452i	$0.649687\pi$
$728$	4.36831e17	−	1.05919e17i	0.108758	−	0.0263705i
$729$	1.39886e18			0.345181
$730$	2.69209e17	+	4.66284e17i	0.0658403	+	0.114039i
$731$	−1.47499e18	+	2.55476e18i	−0.357541	+	0.619280i
$732$	−1.98185e17	+	3.43266e17i	−0.0476155	+	0.0824724i
$733$	5.46187e17	+	9.46024e17i	0.130067	+	0.225282i	0.923702	−	0.383112i	$-0.125148\pi$
$733$	5.46187e17	+	9.46024e17i	0.130067	+	0.225282i	−0.793635	+	0.608394i	$0.791814\pi$
$734$	5.51302e18			1.30126
$735$	1.84697e18	−	9.51620e17i	0.432109	−	0.222636i
$736$	−8.10337e17			−0.187914
$737$	−8.88001e17	−	1.53806e18i	−0.204115	−	0.353538i
$738$	−8.62218e17	+	1.49341e18i	−0.196449	+	0.340260i
$739$	−2.64348e18	+	4.57864e18i	−0.597018	+	1.03407i	0.396241	+	0.918147i	$0.370315\pi$
$739$	−2.64348e18	+	4.57864e18i	−0.597018	+	1.03407i	−0.993259	+	0.115919i	$0.963019\pi$
$740$	5.60057e17	+	9.70047e17i	0.125379	+	0.217163i
$741$	3.70460e17			0.0822096
$742$	−4.28013e18	+	1.03780e18i	−0.941524	+	0.228292i
$743$	−1.06272e18			−0.231736			−0.115868	−	0.993265i	$-0.536965\pi$
$743$	−1.06272e18			−0.231736			−0.115868	+	0.993265i	$0.536965\pi$
$744$	1.20095e18	+	2.08010e18i	0.259597	+	0.449635i
$745$	−1.22673e18	+	2.12475e18i	−0.262865	+	0.455295i
$746$	1.05873e18	−	1.83377e18i	0.224896	−	0.389531i
$747$	−1.05752e18	−	1.83168e18i	−0.222692	−	0.385714i
$748$	6.97049e17			0.145513
$749$	−3.10597e18	−	3.25823e18i	−0.642785	−	0.674295i
$750$	3.06780e18			0.629403
$751$	−4.48188e17	−	7.76285e17i	−0.0911593	−	0.157892i	0.816840	−	0.576864i	$-0.195724\pi$
$751$	−4.48188e17	−	7.76285e17i	−0.0911593	−	0.157892i	−0.907999	+	0.418972i	$0.862391\pi$
$752$	−6.76974e17	+	1.17255e18i	−0.136507	+	0.236438i
$753$	−3.96079e18	+	6.86029e18i	−0.791799	+	1.37144i
$754$	−4.34259e17	−	7.52159e17i	−0.0860668	−	0.149072i
$755$	3.87063e18			0.760549
$756$	−5.13935e17	+	1.74952e18i	−0.100119	+	0.340823i
$757$	−6.71607e18			−1.29716			−0.648578	−	0.761148i	$-0.724636\pi$
$757$	−6.71607e18			−1.29716			−0.648578	+	0.761148i	$0.724636\pi$
$758$	6.83837e17	+	1.18444e18i	0.130949	+	0.226811i
$759$	2.41544e18	−	4.18367e18i	0.458591	−	0.794303i
$760$	8.47205e16	−	1.46740e17i	0.0159478	−	0.0276224i
$761$	3.56938e18	+	6.18234e18i	0.666181	+	1.15386i	0.978964	+	0.204034i	$0.0654054\pi$
$761$	3.56938e18	+	6.18234e18i	0.666181	+	1.15386i	−0.312783	+	0.949825i	$0.601261\pi$
$762$	−9.82481e16			−0.0181810
$763$	−1.39770e18	+	4.75802e18i	−0.256451	+	0.873006i
$764$	−3.11444e18			−0.566595
$765$	1.81533e17	+	3.14424e17i	0.0327458	+	0.0567173i
$766$	−7.13234e17	+	1.23536e18i	−0.127569	+	0.220956i
$767$	−1.26637e18	+	2.19342e18i	−0.224591	+	0.389003i
$768$	−2.10221e17	−	3.64113e17i	−0.0369681	−	0.0640307i
$769$	9.57731e18			1.67002			0.835011	−	0.550233i	$-0.185461\pi$
$769$	9.57731e18			1.67002			0.835011	+	0.550233i	$0.185461\pi$
$770$	8.45672e17	+	8.87128e17i	0.146222	+	0.153390i
$771$	−3.22059e18			−0.552181
$772$	1.31523e16	+	2.27805e16i	0.00223609	+	0.00387303i
$773$	−1.07825e18	+	1.86758e18i	−0.181783	+	0.314857i	−0.942488	−	0.334241i	$-0.891520\pi$
$773$	−1.07825e18	+	1.86758e18i	−0.181783	+	0.314857i	0.760705	+	0.649098i	$0.224853\pi$
$774$	−1.51388e18	+	2.62212e18i	−0.253090	+	0.438366i
$775$	3.11180e18	+	5.38979e18i	0.515882	+	0.893534i
$776$	2.04595e18			0.336351
$777$	8.60706e18	−	2.08695e18i	1.40319	−	0.340233i
$778$	1.39694e18			0.225844
$779$	9.52444e17	+	1.64968e18i	0.152702	+	0.264488i
$780$	−2.41926e17	+	4.19029e17i	−0.0384652	+	0.0666237i
$781$	−1.36729e18	+	2.36822e18i	−0.215590	+	0.373413i
$782$	−9.59012e17	−	1.66106e18i	−0.149962	−	0.259741i
$783$	3.52333e18			0.546389
$784$	−1.36727e18	−	8.79155e17i	−0.210281	−	0.135211i
$785$	−7.62063e17			−0.116235
$786$	−2.95100e18	−	5.11128e18i	−0.446398	−	0.773185i
$787$	1.41242e18	−	2.44639e18i	0.211899	−	0.367020i	−0.740410	−	0.672156i	$-0.765369\pi$
$787$	1.41242e18	−	2.44639e18i	0.211899	−	0.367020i	0.952309	+	0.305136i	$0.0987019\pi$
$788$	−8.59569e17	+	1.48882e18i	−0.127897	+	0.221524i
$789$	−4.30288e18	−	7.45280e18i	−0.634977	−	1.09981i
$790$	−2.25922e18			−0.330661
$791$	−1.47285e18	+	3.57122e17i	−0.213802	+	0.0518406i
$792$	7.15428e17			0.103004
$793$	−1.78438e17	−	3.09063e17i	−0.0254807	−	0.0441338i
$794$	8.42427e17	−	1.45913e18i	0.119316	−	0.206661i
$795$	2.37042e18	−	4.10569e18i	0.332996	−	0.576767i
$796$	−3.08776e18	−	5.34815e18i	−0.430237	−	0.745193i
$797$	8.37611e18			1.15761			0.578806	−	0.815465i	$-0.303519\pi$
$797$	8.37611e18			1.15761			0.578806	+	0.815465i	$0.303519\pi$
$798$	−9.24401e17	−	9.69717e17i	−0.126719	−	0.132931i
$799$	−3.20472e18			−0.435749
$800$	−5.44708e17	−	9.43461e17i	−0.0734647	−	0.127245i
$801$	8.86501e17	−	1.53546e18i	0.118595	−	0.205413i
$802$	−5.12278e18	+	8.87291e18i	−0.679786	+	1.17742i
$803$	1.25562e18	+	2.17481e18i	0.165276	+	0.286266i
$804$	−2.53556e18			−0.331062
$805$	9.50524e17	−	3.23575e18i	0.123109	−	0.419085i
$806$	−2.16257e18			−0.277838
$807$	−6.33122e18	−	1.09660e19i	−0.806881	−	1.39756i
$808$	1.72571e18	−	2.98901e18i	0.218169	−	0.377880i
$809$	1.08897e18	−	1.88615e18i	0.136569	−	0.236544i	−0.789627	−	0.613587i	$-0.789726\pi$
$809$	1.08897e18	−	1.88615e18i	0.136569	−	0.236544i	0.926196	+	0.377043i	$0.123059\pi$
$810$	−1.44787e18	−	2.50779e18i	−0.180127	−	0.311988i
$811$	−1.05998e19			−1.30817			−0.654084	−	0.756422i	$-0.726946\pi$
$811$	−1.05998e19			−1.30817			−0.654084	+	0.756422i	$0.726946\pi$
$812$	−8.85256e17	+	3.01357e18i	−0.108381	+	0.368949i
$813$	−1.26756e18			−0.153950
$814$	2.61217e18	+	4.52442e18i	0.314734	+	0.545135i
$815$	−1.80780e18	+	3.13120e18i	−0.216085	+	0.374271i
$816$	4.97581e17	−	8.61836e17i	0.0590035	−	0.102197i
$817$	1.67230e18	+	2.89651e18i	0.196730	+	0.340747i
$818$	−1.25669e18			−0.146667
$819$	7.53450e17	+	7.90385e17i	0.0872386	+	0.0915153i
$820$	−2.48795e18			−0.285793
$821$	−5.15388e16	−	8.92679e16i	−0.00587360	−	0.0101734i	0.863074	−	0.505078i	$-0.168536\pi$
$821$	−5.15388e16	−	8.92679e16i	−0.00587360	−	0.0101734i	−0.868947	+	0.494905i	$0.835203\pi$
$822$	−6.32626e18	+	1.09574e19i	−0.715287	+	1.23891i
$823$	5.26006e18	−	9.11070e18i	0.590054	−	1.02200i	−0.404170	−	0.914684i	$-0.632440\pi$
$823$	5.26006e18	−	9.11070e18i	0.590054	−	1.02200i	0.994224	−	0.107320i	$-0.0342271\pi$
$824$	−2.31838e18	−	4.01556e18i	−0.258023	−	0.446909i
$825$	6.49463e18			0.717140
$826$	8.90147e18	−	2.15834e18i	0.975195	−	0.236456i
$827$	1.20216e19			1.30670			0.653350	−	0.757056i	$-0.273363\pi$
$827$	1.20216e19			1.30670			0.653350	+	0.757056i	$0.273363\pi$
$828$	−9.84299e17	−	1.70486e18i	−0.106152	−	0.183861i
$829$	−1.57256e18	+	2.72375e18i	−0.168268	+	0.291449i	−0.937811	−	0.347146i	$-0.887151\pi$
$829$	−1.57256e18	+	2.72375e18i	−0.168268	+	0.291449i	0.769543	+	0.638595i	$0.220484\pi$
$830$	1.52575e18	−	2.64267e18i	0.161985	−	0.280566i
$831$	−5.19094e18	−	8.99097e18i	−0.546814	−	0.947109i
$832$	3.78549e17			0.0395658
$833$	1.83996e17	−	3.84313e18i	0.0190816	−	0.398559i
$834$	1.58963e19			1.63575
$835$	3.74308e16	+	6.48321e16i	0.00382180	+	0.00661955i
$836$	3.95147e17	−	6.84414e17i	0.0400330	−	0.0693391i
$837$	4.38646e18	−	7.59757e18i	0.440960	−	0.763765i
$838$	3.91622e18	+	6.78309e18i	0.390644	+	0.676615i
$839$	5.05894e18			0.500734			0.250367	−	0.968151i	$-0.419449\pi$
$839$	5.05894e18			0.500734			0.250367	+	0.968151i	$0.419449\pi$
$840$	1.70052e18	−	4.12327e17i	0.167020	−	0.0404973i
$841$	−4.19166e18			−0.408519
$842$	−7.77878e17	−	1.34732e18i	−0.0752286	−	0.130300i
$843$	8.48911e17	−	1.47036e18i	0.0814672	−	0.141105i
$844$	1.94466e18	−	3.36826e18i	0.185190	−	0.320759i
$845$	1.95628e18	+	3.38837e18i	0.184868	+	0.320201i
$846$	−3.28922e18			−0.308451
$847$	−3.47026e18	−	3.64038e18i	−0.322939	−	0.338770i
$848$	−3.70907e18			−0.342525
$849$	8.16476e18	+	1.41418e19i	0.748244	+	1.29600i
$850$	1.28929e18	−	2.23312e18i	0.117254	−	0.203090i
$851$	7.18775e18	−	1.24495e19i	0.648710	−	1.12360i
$852$	1.95205e18	+	3.38105e18i	0.174837	+	0.302827i
$853$	−1.27122e19			−1.12993			−0.564967	−	0.825114i	$-0.691111\pi$
$853$	−1.27122e19			−1.12993			−0.564967	+	0.825114i	$0.691111\pi$
$854$	−3.63753e17	+	1.23828e18i	−0.0320871	+	0.109230i
$855$	4.11633e17			0.0360355
$856$	−1.89551e18	−	3.28312e18i	−0.164682	−	0.285238i
$857$	−9.91400e18	+	1.71715e19i	−0.854818	+	1.48059i	0.0219964	+	0.999758i	$0.492998\pi$
$857$	−9.91400e18	+	1.71715e19i	−0.854818	+	1.48059i	−0.876814	+	0.480830i	$0.840336\pi$
$858$	−1.12837e18	+	1.95440e18i	−0.0965573	+	0.167242i
$859$	3.16105e18	+	5.47510e18i	0.268458	+	0.464982i	0.968464	−	0.249155i	$-0.0801528\pi$
$859$	3.16105e18	+	5.47510e18i	0.268458	+	0.464982i	−0.700006	+	0.714137i	$0.746819\pi$
$860$	−4.36834e18			−0.368194
$861$	−5.54439e18	+	1.88741e19i	−0.463803	+	1.57887i
$862$	−7.86480e18			−0.652966
$863$	3.01615e18	+	5.22413e18i	0.248532	+	0.430471i	0.963119	−	0.269076i	$-0.0867184\pi$
$863$	3.01615e18	+	5.22413e18i	0.248532	+	0.430471i	−0.714586	+	0.699547i	$0.753385\pi$
$864$	−7.67832e17	+	1.32992e18i	−0.0627953	+	0.108765i
$865$	−1.88880e18	+	3.27150e18i	−0.153314	+	0.265547i
$866$	−4.51377e18	−	7.81808e18i	−0.363641	−	0.629845i
$867$	−1.24391e19			−0.994634
$868$	5.39622e18	+	5.66075e18i	0.428264	+	0.449258i
$869$	−1.05373e19			−0.830041
$870$	−1.69051e18	−	2.92805e18i	−0.132173	−	0.228931i
$871$	1.14146e18	−	1.97707e18i	0.0885814	−	0.153427i
$872$	−2.08820e18	+	3.61687e18i	−0.160848	+	0.278597i
$873$	2.48517e18	+	4.30443e18i	0.190004	+	0.329097i
$874$	−2.17460e18			−0.165027
$875$	9.70763e18	−	2.35381e18i	0.731242	−	0.177304i
$876$	3.58526e18			0.268067
$877$	1.59022e18	+	2.75435e18i	0.118021	+	0.204419i	0.918984	−	0.394296i	$-0.129012\pi$
$877$	1.59022e18	+	2.75435e18i	0.118021	+	0.204419i	−0.800962	+	0.598715i	$0.795678\pi$
$878$	4.70362e18	−	8.14691e18i	0.346512	−	0.600176i
$879$	1.22452e18	−	2.12093e18i	0.0895445	−	0.155096i
$880$	5.16096e17	+	8.93904e17i	0.0374622	+	0.0648864i
$881$	−2.33099e19			−1.67956			−0.839782	−	0.542924i	$-0.817317\pi$
$881$	−2.33099e19			−1.67956			−0.839782	+	0.542924i	$0.817317\pi$
$882$	1.88847e17	−	3.94447e18i	0.0135072	−	0.282126i
$883$	−1.95630e18			−0.138896			−0.0694482	−	0.997586i	$-0.522124\pi$
$883$	−1.95630e18			−0.138896			−0.0694482	+	0.997586i	$0.522124\pi$
$884$	4.48002e17	+	7.75962e17i	0.0315748	+	0.0546891i
$885$	−4.92982e18	+	8.53870e18i	−0.344905	+	0.597393i
$886$	5.98037e18	−	1.03583e19i	0.415345	−	0.719399i
$887$	5.03283e18	+	8.71712e18i	0.346983	+	0.600993i	0.985712	−	0.168439i	$-0.0538727\pi$
$887$	5.03283e18	+	8.71712e18i	0.346983	+	0.600993i	−0.638729	+	0.769432i	$0.720539\pi$
$888$	7.45869e18			0.510479
$889$	−3.10893e17	+	7.53822e16i	−0.0211227	+	0.00512162i
$890$	2.55802e18			0.172532
$891$	−6.75305e18	−	1.16966e19i	−0.452163	−	0.783170i
$892$	−1.24508e18	+	2.15654e18i	−0.0827609	+	0.143346i
$893$	−1.81671e18	+	3.14663e18i	−0.119881	+	0.207640i
$894$	8.16862e18	+	1.41485e19i	0.535124	+	0.926862i
$895$	−5.19803e18			−0.338056
$896$	−9.44585e17	−	9.90891e17i	−0.0609873	−	0.0639770i
$897$	6.20974e18			0.398036
$898$	6.89527e18	+	1.19430e19i	0.438788	+	0.760003i
$899$	7.55571e18	−	1.30869e19i	0.477350	−	0.826795i
$900$	1.32329e18	−	2.29200e18i	0.0830000	−	0.143760i
$901$	−4.38958e18	−	7.60298e18i	−0.273345	−	0.473448i
$902$	−1.16041e19			−0.717412
$903$	−9.73484e18	+	3.31391e19i	−0.597528	+	2.03409i
$904$	−1.27634e18			−0.0777806
$905$	4.85560e18	+	8.41015e18i	0.293784	+	0.508848i
$906$	1.28870e19	−	2.23210e19i	0.774140	−	1.34085i
$907$	6.24089e18	−	1.08095e19i	0.372220	−	0.644703i	−0.617687	−	0.786424i	$-0.711930\pi$
$907$	6.24089e18	−	1.08095e19i	0.372220	−	0.644703i	0.989907	+	0.141721i	$0.0452635\pi$
$908$	5.70609e18	+	9.88324e18i	0.337894	+	0.585250i
$909$	8.38471e18			0.492973
$910$	−4.44037e17	+	1.51158e18i	−0.0259209	+	0.0882393i
$911$	2.22935e19			1.29214			0.646068	−	0.763280i	$-0.276412\pi$
$911$	2.22935e19			1.29214			0.646068	+	0.763280i	$0.276412\pi$
$912$	−5.64143e17	−	9.77124e17i	−0.0324655	−	0.0562320i
$913$	7.11627e18	−	1.23257e19i	0.406623	−	0.704292i
$914$	−1.22851e18	+	2.12784e18i	−0.0696991	+	0.120722i
$915$	−6.94633e17	−	1.20314e18i	−0.0391308	−	0.0677765i
$916$	4.64942e18			0.260063
$917$	−1.32597e19	−	1.39098e19i	−0.736435	−	0.772536i
$918$	−3.63483e18			−0.200451
$919$	−1.24631e19	−	2.15867e19i	−0.682455	−	1.18205i	−0.974229	−	0.225560i	$-0.927579\pi$
$919$	−1.24631e19	−	2.15867e19i	−0.682455	−	1.18205i	0.291774	−	0.956487i	$-0.405754\pi$
$920$	1.42011e18	−	2.45970e18i	0.0772148	−	0.133740i
$921$	−4.25655e18	+	7.37256e18i	−0.229811	+	0.398044i
$922$	1.00891e19	+	1.74748e19i	0.540881	+	0.936833i
$923$	−3.51510e18			−0.187123
$924$	7.93145e18	−	1.92314e18i	0.419261	−	0.101658i
$925$	1.93264e19			1.01445
$926$	−7.31653e18	−	1.26726e19i	−0.381359	−	0.660533i
$927$	5.63218e18	−	9.75522e18i	0.291513	−	0.504916i
$928$	−1.32260e18	+	2.29080e18i	−0.0679775	+	0.117741i
$929$	−1.55121e19	−	2.68677e19i	−0.791713	−	1.37129i	−0.924906	−	0.380197i	$-0.875856\pi$
$929$	−1.55121e19	−	2.68677e19i	−0.791713	−	1.37129i	0.133193	−	0.991090i	$-0.457477\pi$
$930$	−8.41858e18			−0.426678
$931$	−3.66917e18	−	2.35928e18i	−0.184669	−	0.118742i
$932$	−8.35542e18			−0.417604
$933$	6.95399e18	+	1.20447e19i	0.345146	+	0.597811i
$934$	6.81668e18	−	1.18068e19i	0.335984	−	0.581941i
$935$	−1.22157e18	+	2.11582e18i	−0.0597920	+	0.103563i
$936$	4.59815e17	+	7.96422e17i	0.0223506	+	0.0387124i
$937$	4.17037e17			0.0201311			0.0100655	−	0.999949i	$-0.496796\pi$
$937$	4.17037e17			0.0201311			0.0100655	+	0.999949i	$0.496796\pi$
$938$	−8.02344e18	+	1.94545e18i	−0.384629	+	0.0932611i
$939$	−8.43023e18			−0.401340
$940$	−2.37278e18	−	4.10978e18i	−0.112183	−	0.194306i
$941$	9.59391e17	−	1.66171e18i	0.0450467	−	0.0780232i	−0.842623	−	0.538504i	$-0.818990\pi$
$941$	9.59391e17	−	1.66171e18i	0.0450467	−	0.0780232i	0.887670	+	0.460481i	$0.152323\pi$
$942$	−2.53724e18	+	4.39463e18i	−0.118312	+	0.204923i
$943$	1.59651e19	+	2.76524e19i	0.739343	+	1.28058i
$944$	7.71382e18			0.354774
$945$	−4.40984e18	−	4.62602e18i	−0.201426	−	0.211301i
$946$	−2.03745e19			−0.924259
$947$	−1.75162e19	−	3.03389e19i	−0.789158	−	1.36686i	−0.926483	−	0.376336i	$-0.877184\pi$
$947$	−1.75162e19	−	3.03389e19i	−0.789158	−	1.36686i	0.137325	−	0.990526i	$-0.456150\pi$
$948$	−7.52192e18	+	1.30284e19i	−0.336569	+	0.582955i
$949$	−1.61401e18	+	2.79555e18i	−0.0717260	+	0.124233i
$950$	−1.46176e18	−	2.53185e18i	−0.0645169	−	0.111747i
$951$	−1.82407e19			−0.799593
$952$	9.13272e17	−	3.10894e18i	0.0397612	−	0.135354i
$953$	3.82110e19			1.65228			0.826142	−	0.563462i	$-0.190531\pi$
$953$	3.82110e19			1.65228			0.826142	+	0.563462i	$0.190531\pi$
$954$	−4.50532e18	−	7.80345e18i	−0.193491	−	0.335137i
$955$	5.45802e18	−	9.45357e18i	0.232816	−	0.403250i
$956$	7.32462e18	−	1.26866e19i	0.310320	−	0.537489i
$957$	−7.88475e18	−	1.36568e19i	−0.331788	−	0.574673i
$958$	−2.02026e18			−0.0844368
$959$	−1.16114e19	+	3.95271e19i	−0.482017	+	1.64087i
$960$	1.47364e18			0.0607614
$961$	−6.60457e18	−	1.14394e19i	−0.270484	−	0.468493i
$962$	−3.35775e18	+	5.81580e18i	−0.136587	+	0.236576i
$963$	4.60487e18	−	7.97586e18i	0.186057	−	0.322260i
$964$	3.71996e18	+	6.44315e18i	0.149292	+	0.258582i
$965$	−9.21972e16			−0.00367528
$966$	−1.54951e19	−	1.62547e19i	−0.613539	−	0.643615i
$967$	3.71357e19			1.46056			0.730281	−	0.683147i	$-0.239389\pi$
$967$	3.71357e19			1.46056			0.730281	+	0.683147i	$0.239389\pi$
$968$	−2.11783e18	−	3.66819e18i	−0.0827372	−	0.143305i
$969$	1.33530e18	−	2.31280e18i	0.0518171	−	0.0897498i
$970$	−3.58550e18	+	6.21027e18i	−0.138208	+	0.239383i
$971$	5.96924e18	+	1.03390e19i	0.228557	+	0.395872i	0.957381	−	0.288829i	$-0.0932660\pi$
$971$	5.96924e18	+	1.03390e19i	0.228557	+	0.395872i	−0.728824	+	0.684701i	$0.759933\pi$
$972$	−9.94270e18			−0.378158
$973$	5.03017e19	−	1.21967e19i	1.90042	−	0.460795i
$974$	−3.47512e19			−1.30418
$975$	4.17418e18	+	7.22989e18i	0.155611	+	0.269527i
$976$	−5.43456e17	+	9.41293e17i	−0.0201252	+	0.0348579i
$977$	4.03279e18	−	6.98499e18i	0.148351	−	0.256952i	−0.782267	−	0.622943i	$-0.785937\pi$
$977$	4.03279e18	−	6.98499e18i	0.148351	−	0.256952i	0.930618	+	0.365992i	$0.119270\pi$
$978$	1.20379e19	+	2.08502e19i	0.439893	+	0.761918i
$979$	1.19309e19			0.433098
$980$	5.06471e18	−	2.60950e18i	0.182636	−	0.0940997i
$981$	−1.01460e19			−0.363450
$982$	9.18673e18	+	1.59119e19i	0.326916	+	0.566235i
$983$	−1.32814e19	+	2.30040e19i	−0.469511	+	0.813216i	−0.999392	−	0.0348552i	$-0.988903\pi$
$983$	−1.32814e19	+	2.30040e19i	−0.469511	+	0.813216i	0.529882	+	0.848072i	$0.322236\pi$
$984$	−8.28346e18	+	1.43474e19i	−0.290900	+	0.503853i
$985$	−3.01277e18	−	5.21827e18i	−0.105107	−	0.182050i
$986$	−6.26103e18			−0.216993
$987$	−3.64653e19	+	8.84175e18i	−1.25551	+	0.304423i
$988$	1.01586e18			0.0347468
$989$	2.80316e19	+	4.85521e19i	0.952514	+	1.64980i
$990$	−1.25378e18	+	2.17161e18i	−0.0423246	+	0.0733083i
$991$	−1.86864e19	+	3.23658e19i	−0.626682	+	1.08544i	0.361531	+	0.932360i	$0.382254\pi$
$991$	−1.86864e19	+	3.23658e19i	−0.626682	+	1.08544i	−0.988213	+	0.153085i	$0.951079\pi$
$992$	3.29320e18	+	5.70399e18i	0.109722	+	0.190043i
$993$	1.98473e19			0.656950
$994$	8.77116e18	+	9.20114e18i	0.288433	+	0.302573i
$995$	2.16450e19			0.707145
$996$	−1.01597e19	−	1.75972e19i	−0.329759	−	0.571160i
$997$	−7.48500e17	+	1.29644e18i	−0.0241364	+	0.0418055i	−0.877841	−	0.478952i	$-0.841017\pi$
$997$	−7.48500e17	+	1.29644e18i	−0.0241364	+	0.0418055i	0.853705	+	0.520757i	$0.174350\pi$
$998$	1.69416e17	−	2.93437e17i	0.00542757	−	0.00940083i
$999$	−1.36214e19	−	2.35930e19i	−0.433558	−	0.750945i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.14.c.b.11.1	yes	8
3.2	odd	2		126.14.g.b.109.2		8
7.2	even	3	inner	14.14.c.b.9.1	✓	8
7.3	odd	6		98.14.a.j.1.1		4
7.4	even	3		98.14.a.h.1.4		4
7.5	odd	6		98.14.c.o.79.4		8
7.6	odd	2		98.14.c.o.67.4		8
21.2	odd	6		126.14.g.b.37.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.14.c.b.9.1	✓	8	7.2	even	3	inner
14.14.c.b.11.1	yes	8	1.1	even	1	trivial
98.14.a.h.1.4		4	7.4	even	3
98.14.a.j.1.1		4	7.3	odd	6
98.14.c.o.67.4		8	7.6	odd	2
98.14.c.o.79.4		8	7.5	odd	6
126.14.g.b.37.2		8	21.2	odd	6
126.14.g.b.109.2		8	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(32.0000 + 55.4256i) q^{2} +(-746.854 + 1293.59i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-7178.20 - 12433.0i) q^{5} -95597.3 q^{6} +(-302505. + 73348.4i) q^{7} -262144. q^{8} +(-318420. - 551520. i) q^{9} +O(q^{10})\)	\(q+(32.0000 + 55.4256i) q^{2} +(-746.854 + 1293.59i) q^{3} +(-2048.00 + 3547.24i) q^{4} +(-7178.20 - 12433.0i) q^{5} -95597.3 q^{6} +(-302505. + 73348.4i) q^{7} -262144. q^{8} +(-318420. - 551520. i) q^{9} +(459405. - 795712. i) q^{10} +(2.14272e6 - 3.71130e6i) q^{11} +(-3.05911e6 - 5.29854e6i) q^{12} +5.50861e6 q^{13} +(-1.37455e7 - 1.44194e7i) q^{14} +2.14443e7 q^{15} +(-8.38861e6 - 1.45295e7i) q^{16} +(1.98554e7 - 3.43905e7i) q^{17} +(2.03789e7 - 3.52973e7i) q^{18} +(-2.25114e7 - 3.89910e7i) q^{19} +5.88038e7 q^{20} +(1.31044e8 - 4.46097e8i) q^{21} +2.74268e8 q^{22} +(-3.77343e8 - 6.53577e8i) q^{23} +(1.95783e8 - 3.39107e8i) q^{24} +(5.07299e8 - 8.78667e8i) q^{25} +(1.76275e8 + 3.05318e8i) q^{26} -1.43020e9 q^{27} +(3.59345e8 - 1.22327e9i) q^{28} -2.46353e9 q^{29} +(6.86216e8 + 1.18856e9i) q^{30} +(-3.06703e9 + 5.31225e9i) q^{31} +(5.36871e8 - 9.29888e8i) q^{32} +(3.20060e9 + 5.54359e9i) q^{33} +2.54149e9 q^{34} +(3.08338e9 + 3.23453e9i) q^{35} +2.60850e9 q^{36} +(9.52417e9 + 1.64963e10i) q^{37} +(1.44073e9 - 2.49542e9i) q^{38} +(-4.11413e9 + 7.12588e9i) q^{39} +(1.88172e9 + 3.25924e9i) q^{40} -4.23093e10 q^{41} +(2.89186e10 - 7.01191e9i) q^{42} -7.42867e10 q^{43} +(8.77657e9 + 1.52015e10i) q^{44} +(-4.57137e9 + 7.91784e9i) q^{45} +(2.41499e10 - 4.18289e10i) q^{46} +(-4.03508e10 - 6.98897e10i) q^{47} +2.50603e10 q^{48} +(8.61290e10 - 4.43764e10i) q^{49} +6.49342e10 q^{50} +(2.96581e10 + 5.13694e10i) q^{51} +(-1.12816e10 + 1.95404e10i) q^{52} +(1.10539e11 - 1.91459e11i) q^{53} +(-4.57664e10 - 7.92697e10i) q^{54} -6.15234e10 q^{55} +(7.92998e10 - 1.92278e10i) q^{56} +6.72511e10 q^{57} +(-7.88329e10 - 1.36543e11i) q^{58} +(-2.29890e11 + 3.98181e11i) q^{59} +(-4.39178e10 + 7.60679e10i) q^{60} +(-3.23925e10 - 5.61055e10i) q^{61} -3.92580e11 q^{62} +(1.36777e11 + 1.43482e11i) q^{63} +6.87195e10 q^{64} +(-3.95419e10 - 6.84885e10i) q^{65} +(-2.04838e11 + 3.54790e11i) q^{66} +(2.07214e11 - 3.58905e11i) q^{67} +(8.13276e10 + 1.40864e11i) q^{68} +1.12728e12 q^{69} +(-8.06078e10 + 2.74403e11i) q^{70} -6.38110e11 q^{71} +(8.34720e10 + 1.44578e11i) q^{72} +(-2.92998e11 + 5.07488e11i) q^{73} +(-6.09547e11 + 1.05577e12i) q^{74} +(7.57756e11 + 1.31247e12i) q^{75} +1.84414e11 q^{76} +(-3.75965e11 + 1.27985e12i) q^{77} -5.26608e11 q^{78} +(-1.22943e12 - 2.12943e12i) q^{79} +(-1.20430e11 + 2.08591e11i) q^{80} +(1.57581e12 - 2.72939e12i) q^{81} +(-1.35390e12 - 2.34502e12i) q^{82} +3.32114e12 q^{83} +(1.31404e12 + 1.37845e12i) q^{84} -5.70103e11 q^{85} +(-2.37717e12 - 4.11739e12i) q^{86} +(1.83990e12 - 3.18679e12i) q^{87} +(-5.61701e11 + 9.72894e11i) q^{88} +(1.39203e12 + 2.41106e12i) q^{89} -5.85135e11 q^{90} +(-1.66638e12 + 4.04047e11i) q^{91} +3.09119e12 q^{92} +(-4.58125e12 - 7.93495e12i) q^{93} +(2.58245e12 - 4.47294e12i) q^{94} +(-3.23183e11 + 5.59770e11i) q^{95} +(8.01928e11 + 1.38898e12i) q^{96} -7.80467e12 q^{97} +(5.21572e12 + 3.35371e12i) q^{98} -2.72914e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 256 q^{2} + 182 q^{3} - 16384 q^{4} + 1792 q^{5} + 23296 q^{6} - 268352 q^{7} - 2097152 q^{8} + 599840 q^{9}+O(q^{10}) \) 8 * q + 256 * q^2 + 182 * q^3 - 16384 * q^4 + 1792 * q^5 + 23296 * q^6 - 268352 * q^7 - 2097152 * q^8 + 599840 * q^9	\( 8 q + 256 q^{2} + 182 q^{3} - 16384 q^{4} + 1792 q^{5} + 23296 q^{6} - 268352 q^{7} - 2097152 q^{8} + 599840 q^{9} - 114688 q^{10} - 8726914 q^{11} + 745472 q^{12} + 1438416 q^{13} + 27004544 q^{14} - 136873212 q^{15} - 67108864 q^{16} - 7943068 q^{17} - 38389760 q^{18} - 215706806 q^{19} - 14680064 q^{20} - 414124312 q^{21} - 1117044992 q^{22} - 61927978 q^{23} - 47710208 q^{24} - 1327844792 q^{25} + 46029312 q^{26} - 3268643812 q^{27} + 2827460608 q^{28} - 6325846064 q^{29} - 4379942784 q^{30} + 6113775570 q^{31} + 4294967296 q^{32} + 25235960652 q^{33} - 1016712704 q^{34} + 41542225382 q^{35} - 4913889280 q^{36} - 3945652880 q^{37} + 13805235584 q^{38} - 23545599116 q^{39} - 469762048 q^{40} + 86378579952 q^{41} + 16061065216 q^{42} - 109074124256 q^{43} - 35745439744 q^{44} - 104964468168 q^{45} + 3963390592 q^{46} - 3141202722 q^{47} - 6106906624 q^{48} + 151080461672 q^{49} - 169964133376 q^{50} - 241278267462 q^{51} - 2945875968 q^{52} + 149625680376 q^{53} - 104596601984 q^{54} + 174912009748 q^{55} + 70346866688 q^{56} - 128207489960 q^{57} - 202427074048 q^{58} - 866297313938 q^{59} + 280316338176 q^{60} - 477908594184 q^{61} + 782563272960 q^{62} + 953051390564 q^{63} + 549755813888 q^{64} - 1099748343120 q^{65} - 1615101481728 q^{66} + 1895501016278 q^{67} - 32534806528 q^{68} + 3503301895632 q^{69} + 1443396653440 q^{70} + 638832672128 q^{71} - 157244456960 q^{72} - 2966596192756 q^{73} + 252521784320 q^{74} - 1331079867376 q^{75} + 1767070154752 q^{76} + 6943031627392 q^{77} - 3013836686848 q^{78} - 6505959677634 q^{79} + 30064771072 q^{80} + 2449216493684 q^{81} + 2764114558464 q^{82} - 3379817135968 q^{83} + 2724161355776 q^{84} - 16684556982464 q^{85} - 3490371976192 q^{86} - 5273311164492 q^{87} + 2287708143616 q^{88} + 9586601667468 q^{89} - 13435451925504 q^{90} + 16069253407200 q^{91} + 507313995776 q^{92} - 14195747226896 q^{93} + 201036974208 q^{94} + 14384410136978 q^{95} - 195421011968 q^{96} - 44560735311568 q^{97} - 2146516623104 q^{98} + 24706419985464 q^{99}+O(q^{100}) \) 8 * q + 256 * q^2 + 182 * q^3 - 16384 * q^4 + 1792 * q^5 + 23296 * q^6 - 268352 * q^7 - 2097152 * q^8 + 599840 * q^9 - 114688 * q^10 - 8726914 * q^11 + 745472 * q^12 + 1438416 * q^13 + 27004544 * q^14 - 136873212 * q^15 - 67108864 * q^16 - 7943068 * q^17 - 38389760 * q^18 - 215706806 * q^19 - 14680064 * q^20 - 414124312 * q^21 - 1117044992 * q^22 - 61927978 * q^23 - 47710208 * q^24 - 1327844792 * q^25 + 46029312 * q^26 - 3268643812 * q^27 + 2827460608 * q^28 - 6325846064 * q^29 - 4379942784 * q^30 + 6113775570 * q^31 + 4294967296 * q^32 + 25235960652 * q^33 - 1016712704 * q^34 + 41542225382 * q^35 - 4913889280 * q^36 - 3945652880 * q^37 + 13805235584 * q^38 - 23545599116 * q^39 - 469762048 * q^40 + 86378579952 * q^41 + 16061065216 * q^42 - 109074124256 * q^43 - 35745439744 * q^44 - 104964468168 * q^45 + 3963390592 * q^46 - 3141202722 * q^47 - 6106906624 * q^48 + 151080461672 * q^49 - 169964133376 * q^50 - 241278267462 * q^51 - 2945875968 * q^52 + 149625680376 * q^53 - 104596601984 * q^54 + 174912009748 * q^55 + 70346866688 * q^56 - 128207489960 * q^57 - 202427074048 * q^58 - 866297313938 * q^59 + 280316338176 * q^60 - 477908594184 * q^61 + 782563272960 * q^62 + 953051390564 * q^63 + 549755813888 * q^64 - 1099748343120 * q^65 - 1615101481728 * q^66 + 1895501016278 * q^67 - 32534806528 * q^68 + 3503301895632 * q^69 + 1443396653440 * q^70 + 638832672128 * q^71 - 157244456960 * q^72 - 2966596192756 * q^73 + 252521784320 * q^74 - 1331079867376 * q^75 + 1767070154752 * q^76 + 6943031627392 * q^77 - 3013836686848 * q^78 - 6505959677634 * q^79 + 30064771072 * q^80 + 2449216493684 * q^81 + 2764114558464 * q^82 - 3379817135968 * q^83 + 2724161355776 * q^84 - 16684556982464 * q^85 - 3490371976192 * q^86 - 5273311164492 * q^87 + 2287708143616 * q^88 + 9586601667468 * q^89 - 13435451925504 * q^90 + 16069253407200 * q^91 + 507313995776 * q^92 - 14195747226896 * q^93 + 201036974208 * q^94 + 14384410136978 * q^95 - 195421011968 * q^96 - 44560735311568 * q^97 - 2146516623104 * q^98 + 24706419985464 * q^99

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